There is a lot of confusion on how to obtain this achievement, so after unlocking it, I thought I would share what I did to unlock it. This is not going to be a start to finish walkthrough, but rather clear up some areas where people seem to be confused. Also there may be other ways to unlock this, but this is exactly what I did, and it unlocked it for me. There are some minor spoilers in here such as names of enemies and such, so be warned if you haven't played the game yet.
First just a few rules to keep in mind
You CAN kill the people in the dream sequence during the prologue.
You DO NOT have to sneak up undetected on an enemy to knock them out.
You CAN loot air filters off knocked out enemies, this will not count as a kill.
Setting off an alarm will NOT void the achievement.
You CANNOT kill the bandit leader who is holding the woman and children hostage.
You CANNOT kill any of the enemies on the chase level.
You CANNOT kill any of the snipers on red square
You CANNOT kill any of the enemies on D6, until the flame thrower and riot shield enemies appear.
!!MOST IMPORTANT!! be very careful around the enemies, one kill will screw this up. You can't load a check point, and replaying the chapter will not fix it. You must start a new game. An accidental kill late in the game means starting fresh, so be very careful unless you want to lose hours of hard work.
Some simple tips
Play the game on easy. On higher difficulties the enemies will notice you easier, and deal more damage. If you are trying to charge through a hail of bullets and knock an enemy out, you really don't want to die to easy. I am not saying this can't be done on a higher difficulty, but why have the frustration.
Try to take a stealthy approach throughout the game. While it is not required for the achievement, remaining undetected will make your life easier. Remember if you do set off an alarm, you can still run up to the enemies and knock them out, but they will be shooting at you, so make you sure you have plenty of med packs. Honestly though if you have played through the game once you can move pretty fast through the levels, and never get noticed.
If you aren't trying to go for the good ending, you can ignore most of the flashpoints, and optional objectives. This will save a lot of time, and for me unlocked the bad ending, making the second play through worth while.
Level tips
Most of the games levels are pretty simple to navigate without killing anyone, but there are a few levels that force you into a gunfight. You might think it is safe to kill these people, but you would be wrong. Here is how to get past them.
-Bandits- Ok these two may seem simple, but there has been some confusion so I thought I would clarify. A few people have said that they cannot knock the guy out who is standing on the hand cart, thus preventing the levels progression. All I can say is knock out everyone else in the area first, then approach from the left side of the cart, and keep hitting X, sometimes the prompt is there, sometimes not but you should knock him out.
*Note, though I haven't had any issues, it seems that when the guy in the cart is standing up is when people cannot knock him out. Mr. XBob has pointed out that if he is standing up, blowing out the lamp will cause him to turn around, afterwards he will sit back down which will make it easy to knock him out.
When you are rescuing the woman and children towards the end of the level, you will bust through the door and the bandit leader will attack you. There will be a short cut scene of you two struggling, and then you will push him back and you will regain control. Do not shoot him, immediately rush him and hit X to knock him out. If you are ignoring optional objectives, just continue down the rails, ignoring this completely, it is not required to complete the level.
-Chase- The chase level is very confusing, as you have enemies shooting at you and no where to hide. But still, the game does not want you to kill anyone. On my first play through, this was the only place I killed anyone and I still didn't unlock it. Here is what you need to do.
Make sure you have five med packs to heal yourself, this is also why I suggest playing on easy as you will take a lot of damage, and I cannot promise you will make it on higher difficulties. When the level starts, you will be side by side with two cars with Reds shooting at you. Duck down, and just wait them out, you will probably use one or two med packs here. After a bit, Khan will shoot at an oncoming car, and it will explode and flip over you. Then another two sets of cars will appear at your side. Again duck down, and be ready with your med packs. After they leave there will be a heavy gunner at the back of the train, he probably won't damage you much, but if he does, use a med pack. You will then be at the side of the train where 4 Reds will be shooting at you. Just stay ducked and be ready with the last of your med packs. After about 30 seconds, Khan will tell you to jump. At this point you will be on the train, just charge the enemies knocking them out with X as you go. Make sure to loot the bodies, as there will be 2 or 3 med packs to grab, which you will probably need. Just keep knocking them out until you reach the Dark One, even the heavy can be taken out this way, so there is no reason to shoot.
-Red Square- Towards the end of Red Square Pavel and some snipers will start attacking you. Again this is not a place you can kill anyone. After Pavel starts talking run back to rear of the area. There is a barricade with quite a few metal plates here. You will be safe for the most part here. When the snipers first come out, the Dark One will spot them for you, just stayed ducked inside for now. The second time he spots them, you will notice four of them have come downstairs. Wait for them behind the barricade, and knock them out as they come around the corner. You may need to use a med pack or two.
Now, another waiting game begins. Pavel will ramble on for a bit about how you should have joined him blah, blah, blah for about 30 seconds, and he will eventually say he is bored and send some men out to get you. At this point charge across the map to where the doors opened. Be careful as the snipers are still in the windows, so have some med packs handy. Now a heavy, and two regular enemies are at the door, knock them out, and chase Pavel up the stairs. It is ok to shoot him here to make him run. When you get upstairs the snipers will be gone, so you only have Pavel to worry about. Keep shooting him till he finally runs off for the last time. When you approach him the Dark One will meld with him, and then he will be suspended on the wall of hands thing. You NEED to save Pavel here, or it will count as a kill. Simply approach him, and you will automatically pull him down.
*Note, some people have said that shooting at Pavel will cause him to send the guys out of the door faster. He can be easily noticed as he is the only one with a red laser, the others are using a green laser. I did not try this, as I did not want to risk a random head shot on a sniper, since he tends to hide near them. But if you feel safe doing this, it will not void anything, as you will not kill him.
D6- The last, and probably easiest part. The level is going to hand you tons of guns and ammo, and all the free customizations you want. Sadly, you only get to kill a few people. During the first wave, hide and let all your team mates kill the enemies, don't worry the Reds won't hop the barricade. After an explosion you will be down on the ground and Ulman will be pulling you Army of Two style, again do not shoot anyone. You will then be behind another barricade, where you guessed it, do not shoot, and let your team mates take them out. After all this a Tank will fire on you. Grab the Preved sniper rifle to the left, here you must make sure you only fire at the tank, do not shoot any of the troops. Take out it's wheels, then the gun, and it will explode. You will then fall back to the final barricade. Resist the temptation to try out the mini gun and again hide and let your team mates take out the Reds. Eventually a man with a flamethrower will appear guarded by a bunch of guys carrying riot shields. At this point go nuts, kill, that is if Artyom can even remember how to use a gun. There is no limit on how many riot shield guys you can kill, but remember, if the flamethrower guy gets to close you lose. Once you kill the Flamethrower guy, the ending sequence will start and you should see the achievement pop with whatever other end game cheevs you were going for (good/bad ending, etc).
I tried to cover everything that I felt and/or read caused people confusion, but if you would like to see another section added, or a current one broken down further, please post in the comments below and I will add to it, or feel free to P.M. me and I will help you out.
Also, if you discovered another way to obtain this other than mine, (places where you could get a kill, letting Pavel die, etc) please let me know, and I will also add that.
Thanks for taking the time to read this, I hope it helped.