This guide will get you multiple achievements at once. I'll tell you the tips for where you may have the most trouble in each mission. This is not meant to be a detailed walkthrough. This guide just concentrates on getting both checkmarks at the end of each level. I use the word "bodies" but you should not kill anyone at all (for another achievement).
Mission 1, Dishonored: Hide the first three bodies in your cell, there is a guard that patrols a walkway overhead that might see them if you leave them anywhere else. The guards are pretty easy to sneak up on until you get the bomb. As soon as you do that, follow the guy through the door and head right. Carefully come up behind the guard on that side and take his key when the other guard is not looking your way. When you get to the room with the pipes, the patrolling guard and the two guard posts make your way to the pipes and up onto them as soon as you can. In the next room, take out the guard up the stairs first by dropping down behind him when he walks away. Keep to the right wall as you hop the end of the balcony to get behind the other guy, he is facing at a weird angle and easily sees you if you are not right up against the wall. Take both bodies and put them in the dog container just inside the door. When you plant the bomb, hide in the dog container up there. It helps the guards rushing in from the other end not see you. Jump off the left end of the platform into the water and stay under until you get to the rocks that lead to the sewer. There are no guards in most of the sewer and the traps can all be disarmed easily with a little effort by getting to the bolt launcher and taking out the ammo. The only guard you need to worry about is below you after you loot the car. Once he is down, get in the water and follow the marker to the end. There is one guard that walks around near where you come up, but he is not likely to see you if you come out on the same side of the water he is on.
The Hound Pits Pub: The only thing I want to say here is that the game is only slightly more challenging with only Blink level 1, so don't feel that you have to upgrade anything to be successful. Actually, there is an achievement for not getting anything but Blink level 1. Note that you can upgrade anything with Piero that you want to, only powers count. The upgrades to yourself personally, like your mask and boots make things a lot easier.
Mission 2, The Overseer: Guards like to say "huh?" a lot, this does not mean they saw you. You can rescue Griff stealthily, just take out the first guy while he pees and the other one when he faces away. They don't really see you as a threat. The alley just past the rooftop Griff stands under is easily traversed via the pipes and then the girders underneath where the stairs are. Going up the stairs to the right, you can Blink past the arguing guys and then Blink to the green balcony as soon as you go up the next set of stairs. This is a good place to stash bodies, most of the guards go into the guard post below if you are patient allowing you to take them down from a cover location easily. Once you enter the door, the Overseer talking to Martin is too busy to notice you. Once you get above the gate, the light posts are great Blink targets to get around unseen. The staircase on the left just past the gate is where you want to go. Once you get into the building, take the door marked Kennels. If you are lucky, you can get one guard peeing when you enter the room to the right. The guard with the dog is a bit unpredictable and there is at least one more guard in this area. Just be aware of the footstep sounds and you should be fine. The guards in the next area all like to come look at the painting just outside the stairway door, giving you a great opportunity to knock them out one by one. When they stop coming go upstairs and Blink up to the window above the door and use the hanging lights to make your way to the library to find out how to brand someone. You will be in here a while, the best strategy is to take out each guard as they come in and then hide them in one of the office areas upstairs. Note that there are two upstairs already that you should go after first. Once they stop coming, go read the book that your goal marker points to and make your way to the Meeting Room. If you promised to save Curnow, dump out the glasses. Blink up to one of the window ledges and wait. Take Curnow down as soon as the pair leaves the room and hide him near the open window. Follow your target downstairs and knock him out so you can carry him back upstairs. You should have the key to the room with the brand from one of the guards, so go get that and do what you need to do. Go get Curnow and follow the ledges around to the safe area. Blink down and put him in the trash bin when the coast is clear and then enter the next door. You can knock out the guard at the top of the stairs and then sleep bolt the other one without being noticed. The next guard won't come down the stairs, so just follow him and knock him out. At the next door, be careful of the guard and the dog. After they walk away from you, Blink up to and across the rooftops to get to the water where Samuel waits for you.
The Hound Pits Pub: Being seen by the weepers in the sewer does not count against any achievements, but killing them does.
Mission 3, The Golden Cat: When you are doing Slackjaw's mission to find his friend, the best way in is through the second floor balcony. You can use the rooms that parallel the rooms that the guards stand in to get the best of them. You can't really rescue the lady without being detected, but I really don't suggest going to the Art Dealer's house on this run. If you are careful, you can Blink to the second floor in the Captain's Chair hotel without having the rats chase you if you climb the stairs. After you cross over the big white courtyard, sleep bolt the guard on the balcony to your right. Open the closed window shutter to get the combination from the Art Dealer. Now you need to go back out and into the other window. Get the key and rescue Emily but don't follow her out. The best way out is the way you came in, if you did not manage to take out the weepers without being seen.
Mission 4, The Royal Physician: Blink across the water from the wooden ramp to the stairs. Carefully take out the guy in the guard booth and then carefully Blink up behind the guy looking over the wall and get him. There are no guards in the warehouse. On the other side of the area, where the railcar takes you, you can carefully take the guards down one at a time or sneakily make your way to the left and go into the door. In the next area, you should Blink up behind the guy as he enters his house before he locks the door. Close the door and use his rooftop to advance. Take out the guy on the next balcony and keep going straight across from there to get to the first area with Arc Pylons. Wait for the guards to take out two thugs and then stay on the right side of the area and Blink on top of the guard station to avoid the guards and the Pylons. One way to get up to the area you need on the bridge is by jumping off into the water and then blinking up onto the area near the fence. Once there, just avoid the guards on that level and climb the stairs carefully. Disable any Pylons you come across as you climb, the whale oil ports are usually along the way. When you climb a staircase and see yellow, you are near the guard with the key to the next bridge. Wait for him to come downstairs and quickly take him down. You can make it most of the way to the next goal from the end of the newly raised bridge. Once the oil is removed, use one of the two big white chains to get to the other end of the area. As noble as it is to want to free the innocents in the cage, it is hard to do without being seen. The best way to go is through the house on the right as you enter the area and using the rooftops. You can sleep bolt the guard on the roof of Sokolov's house and he won't fall. Blink over there and then go inside and get Sokolov. Knock him out and feel good about yourself if you want to free the prisoner up here. With him on your shoulder, Blink across to the rooftops and down to the ground and then toward the stairs that lead to Samuel.
Mission 5, Lady Boyle's Last Party: There are two ways in to begin the main mission. The first way is to go right and Blink up to the metal platform and then from there to the balcony where the weeper is and then to the rooftops and then across the bridge near the two guards. Once there, Blink up to the balcony and then drop down into the neutral street and use your invitation, or the woman's invitation that she drops, to get inside. The other way requires you to cross the other bridge and go around the back of the building to Blink to a balcony and then you can Blink into the courtyard of the house. Once inside the house, find the man in the ugly rat mask and then go talk to the woman in the fly mask. Tell your target that someone is going to kill her and then go down with her and knock her out. You can leave her there and go back upstairs. Hopefully the room you come out in belongs to your victim, if not you will have to take out all the guards on this floor to find a key you need for the next mission that is in one of the other bedrooms. Once you have it, go back downstairs and once you get her on the boat, take the sewer exit and swim with all your might to Samuel before the gate closes. If you don't make it and have to go by land, there is a staircase behind the Tallboys that will get you past them.
Mission 6, Return to the Tower: Blink up into the alcove on the right and then carefully Blink past the rotating wheels. Blink across to the other side and then Blink onto the balcony but don't open the door. Blink into the big hole in the wall and then follow the pipes. Take cover from the Tallboy and then Blink quickly up the pipes, onto the wall and onto a black beam. From there, get on top of the bridge and make your way across the construction zone. Get over the wall and wait for a guard to come pee so you can knock him out. Enter the opening to the left and be careful of a guard who patrols a little higher up. You can sleep bolt him if you are careful but it is better to get him from behind after he walks away. There is one more guard in the area and you can sleep bolt him. Follow the ledge to a flap that lets you into the building. Go right while the conversation goes on and then go through the door on your right. Go down and disable the Arc Pylon first thing and then go up and talk to the announcer who gives you the combination to a safe. Enter the room and open the safe and get the audiolog and leave quickly. If you hear him talking about wanting tea, he is about to come into the room. You can actually come and go from the room via the chandeliers and avoid the door to this room altogether. Go back upstairs and plug the log in. Now just wait a little bit for them to arrest him and then go back out the way you came in.
Mission 7, Flooded District: Use the stones to destroy the wood and Blink out. Get everything you can and then Blink across and go downstairs and get more. You can go upstairs now and try to avoid the assassins seeing you while you take them down. Or you can jump in the water and swim toward your objective marker and blink past a grate and get nibbled a little bit. Climb the chain on the left side when you get to it and stay on it so you can Blink from the top of it to the nearby roof. Go toward the goal marker for your items and then patiently wait for the weepers to separate so you can take them down one at a time. I've found if you sneak by them then by the time you get back they have gathered around the fire and are staring at the door you come back in from. If they do gather at the fire before you leave this area, you may be able to show yourself for a moment to get one white point that will cause one of them to move. In the next area, the best way to go is out the right window and across the rooftops and vents. Carefully Blink down to the ground on the far side and explore the area to find an oil canister to fill and power the stairs. When you get to the chain inside, the weepers may see you if you stay there. If the one by the fire is facing away, go get him first and then wait for the female one to pass by. If he is not, wait for her to pass by and follow her up the stairs to take her down first. At the bottom, the only enemy should be Campbell as a weeper. His movements are a bit erratic, but you should be able to get him knocked out and get your stuff. After you turn the wheel upstairs, Blink to the right and go around the building to get back to where you entered the area. Blinking onto the broken roof can be a bit of a targeting nightmare, but be patient. When you come back out, be careful of the two assassins that are now on the rooftops. You can sleep bolt the one farther from you when he is behind the square corner, but I suggest you save before you shoot him just in case. In the area with the door you need there is one on the right rooftop, one on the left rooftop and one on the ground. It's a good idea to get them all to avoid being seen. If you are especially good at sneaking, you can go right to the door. You should have found the key on the first assassin in this area after you got back from the refinery. In the next area, the best way to proceed is by water. There are no fish here. Swim into the left alley and make your way up and into the building. Wait for the assassins to move around a bit and Blink forward out of the window. Immediately Blink up onto the chimney you see there and onto the rooftop nearby. Wait until the assassins start talking and then go around the corner and you can see the window you need to enter. You can Blink directly inside that window even with level 1. You have to pay very close attention to be sure the target lands inside, if you land outside the window one assassin may see you. Ignore the door right now, it's locked. Cross the area and get on a shelf. The assassin stops and stands against the wall for a moment before heading into visual range of the other one. You need to get him before he gets over that far or wait until he comes back. Next is a little trick I accidentally discovered that comes in useful later. Wait for the other assassin to head into the other room. If you look carefully, you can see his back under the window. Shoot him through the crack. Proceed carefully and wait for the student to be sent home before you knock out his teacher. Outside, go into the right window and then head left after the assassin goes in to give his report. Carefully sneak up and knock out the assassin in the room on that side, he might mess up this next part. Go back outside Daud's office on the left side and look into the crack under the window. Sleep bolt the assassin there, then back away from the window. This upsets Daud, but he cannot see you if you did not open the door and he will calm down shortly. Once he does, go around to the other door and Blink to the stairs. Now get on the bookshelf there and wait for him to start reading. Immediately Blink behind him and knock him out. Now retrace your steps to the open window and the locked door. Make your way down the chain and through the sewers. Once outside, go left and make your way up the broken pieces to a set of buildings you can cross back and forth between. On the roof Blink down to the pillar above the tracks near where the train stops. Hop on board. If you upgraded your mask well, you can hit the whale oil with a normal crossbow bolt to open the Wall of Light. If you did not, you will need to get off on the left there and take the oil out. Then just hop down and go out the door. Go into the building on the left to avoid some weepers and then open the sewer grate when you get to it. You're now in the sewers. It's pretty linear, and remember killing River Krusts does not count against your no killing achievements.
Mission 8, The Loyalists: Wait for the conversation outside the apartment to end and then make Blink way to the awning to the left. Blink onto the light and then across the street to the open window. This puts you on the second floor and the enemies should not be here yet. Go into the Admiral's office and get the blueprints from the trash can. Now go up the stairs and carefully peek into the room outside of your bedroom. Go out the window when the guard there is not looking. Blink down to the walkway on the far side that leads to Piero and Sokolov. Talk to them twice to have them tell you to put a whale oil tank on the roof, after you tell Piero to knock everyone out. Carefully avoid the view of the Tallboy who is walking around outside Piero's front door as you climb the vent and then be careful of the other one as you jump up onto the roof. Once the thing is activated, feel free to loot the area and get the note from the bar. Go to Emily's room and knock on the door and then trigger the rocket. Go out the other door and down behind the tower to meet Samuel.
Mission 9, The Light at the End: Once you land, head right and swim over to the cliff where the guard post is. Blink up there and stand on top of the guard post to knock out the standing guard when the other one walks away. Take him with you when you Blink to the sewer entrance. Leave him inside and he will be fine. Carefully take out the two guards in the next area and turn the wheel that opens the way into the next area. This will put you at the very bottom of the stairs that lead where you need to go. Carefully take out each guard as you come to them. Don't climb the chain, you will probably be seen. At the top, Blink up to the left big chain and follow it over to the elevator. Be careful of a couple of guards who might see you if you move too fast. You can either get the key from one of them, or go all the way upstairs on that end and jump into the top of the elevator. When you reach the top, you can get out of the elevator the same way or exit the door and then Blink on top of the elevator. Blink up the rafters until you reach the outside of the lighthouse and carefully make your way along the edge. Blink to the balcony when you get to that end and sleep bolt Havelock when you see him. Go get the key and free Emily. Game over, congratulations.