First off let me state that as of the time I am writing this I have not yet gained the achievement. I attempted it on my first playthrough of the game and somewhere among the hours I made a boo boo. As I have had many conversations about the game, I figured I would compile as much information about this achievement to give myself and anyone reading this a better shot at obtaining it. I am not claiming whole credit of this solution as most of this information is from a variety of sources, a list too long to write down. I am not worried about the votes whatsoever; I just hope this helps with anyone attempting Foxiest of the Hounds. Now to what will most likely be a lengthy solution!
Foxiest of the Hounds is obtained by not tripping an alarm the entire way through Deus Ex: Human Revolution. You will know that you have not tripped an alarm by receiving the smooth operator bonus at the end of each section it is possible for. There is also the ghost bonus which is given by having not a single enemy seeing you. The Ghost bonus does not count towards Foxiest of the Hounds. However, soldiers not seeing you decreases the chances of them setting off alarms. The easiest way I can see this being done is it being the sole achievement that you are going for. By that I mean the less risk you take, the better off you are. I will list each area and mission and section that has the potential of the smooth operator bonus later in this solution. Now on to alarms.
Alarms can come from a number of different sources be it:
1. Being spotted by a camera/turret
2. Spotted by a soldier who runs and activates a wall alarm
3. Failing a hack on a floor that has a sentry bot
4. Walking through wall lasers
5. Hacking a security system and having bot/turret attack enemies
These are the confirmed ways to trip an alarm. There have been other concerns as to soldiers going hostile or the crazies going hostile. According to multiple sources as long as a soldier does not hit an alarm they can go hostile. Being in the alarmed state for both is fine. If they go hostile for a split second before you knock them out you will be fine as well. Obviously bosses going hostile do not count as none of them trigger an alarm. Also, there are many scripted alarms that do not stop you from getting this achievement. As well, neither do the alarms that go off in decontamination chambers. It is unconfirmed if civilians can set off alarms. I know from my own playthrough that civilians will react, by cowering on the ground or running away and screaming, if they see you knock out a guard or see a body on the floor. I do not know if they can trigger alarms. They will also react if they see you. Since I cannot tell you whether or not they can, let's just say we should avoid them all together just in case.
Failed hacks do set off alarms. I have confirmed this personally on areas that have a guard bot that is kept behind a door that literally says "Sentry Bot." The alarm is barely audible and even once it didn't sound, but the sentry bot still came out so be careful when hacking. If it looks like you are going to be caught disconnect and try again.
THE LAST BOSS FIGHT YOU DO NOT HAVE TO DO STEALTHY. I want to make that clear because there are turrets and in some areas cameras, however they have nothing to do with Foxiest of the Hounds.
Mines do not count as alarms. They will get the attention of soldiers which will not cause them to directly go into an alarmed state. I will admit that I didn't know that they could be deactivated. Yes, I know, I am an idiot, but by slow walking or even better crouching, you can deactivate them by pressing x. Once deactivated you can take them and use them at a later time, which will help you immensely as I will describe later on. I was throwing boxes and barrels to make them explode. Deactivating them will not cause this which means we can add another level of stealth. Also, mines come in handy against the bosses when running any set-up.
Now for the missions that I can confirm you need to get Foxiest. Next to the mission sections I will denote whether or not you can get ghost by putting (Gh) and smooth operator by (SO).
1. Retrieve the Dead Terrorist's Neural Hub (will sometimes work by convincing Wayne Haas to let you in. On my first playthrough I got SO, on the second I didn't. If you don't and need to infiltrate I suggest going by the sewers it is much easier than the other two access points)
2. Locate and shut down the antennae in Derelict Row (Gh)
1. Infiltrate the mercenary compound (Gh) (SO)
2. Locate the mercenary leader (Gh) (SO)
1. Investigate the Penthouse Apartment (Gh)
2. Find and speak with Tong Si Hung (Gh)
3. Escape the Alice Gardens Pods ambush (Gh)
Tai Yong Medical
1. Enter TYM's tower by passing through the Pangu (Gh) (SO)
2. Find and view Van Bruggen's recording (Gh) (SO)
3. Confront Zhao in the Penthouse (Gh) (SO)
4. Escape and get to the hangar (Gh) (SO)
5. Open the hangar door (Gh) (SO)
1. Escape the ambush by reaching a lower floor (Gh) (SO)
2. Get to the funicular (Gh) (SO)
3. Summon the funicular (many sites and even the guide will tell you that it is possible to get smooth operator here, it isn't possible. I didn't get it and my achievement still popped. I suggest staying hidden anyways)
4. Get inside room 802-11 (Gh) (SO)
1. Go to the convention center and obtain Sandoval's location from Taggert (can be done through conversation or sneaking into his backstage room) (Gh) (SO)
2. Find and confront Sandoval (Gh) (SO)
1. Escape the construction site (Gh) (If you are trying to save Faridah Malik then by all means go right on ahead. It will not affect Foxiest in anyway shape or form.)
2. Find Vasili Sevchenko's GPL device (No ghost nor smooth operator)
3. Rescue Tong's Son (This is a pre-order DLC from Gamestop. If you have it you can get ghost and smooth operator. If you don't have it, it obviously doesn't affect you.)
4. Meet Tong in the Harvester Hideout (No ghost or smooth operator)
1. Retrieve Tong's package from the shed (Gh) (SO)
2. Place the C4 on the administrator's desk (Gh) (SO) (you will not see these bonuses pop up because it cuts straight to a cutscene. It worried me at first, but I pressed on. If you are 100% sure you didn't trip an alarm keep going. I suggest making a save file before you enter the building.)
1. Disable the signal jammer (Gh) (SO, the only way I found to get this smooth operator bonus was to do it in the first building you see once you leave the storage shed you wake up in. If you try and disable it from the tower you will most likely not get it. I didn't receive it the two times I tried on the tower, but I got it the first time I disbaled it in the building. This will enable this SO and the search for signs of Megan's team SO.)
2. Search for signs of Megan's team (Gh) (SO) (see above)
3. Find and speak with Nia Colvin (no ghost and no SO)
4. Find and speak with Eric Koss (no Gh and no SO)
5. Find and speak with Declan Faherty (no Gh and no SO)
6. Upload the virus to the security computer and enter the restricted area (Gh) (SO)
7. Use the Leo Shuttle to reach Panchea (Whether you save Malik or not there is no bonuses here so feel free do handle this section as you like)
1. Get inside the tower and disengage the lockdown (Gh) (SO)
2. Reach the broadcast center (Gh) (SO)
After playing through a second time, the side missions do not have stealth bonuses so feel free to play them without any fear of messing up Foxiest.
The Sarif Manufacturing Plant does not have a smooth operator bonus, but it does have a Ghost bonus. Also, the prologue does not have a smooth operator bonus, but it is highly debated on whether or not it counts, so go ghost.
The end of Tai Yong Medical there are 2 sentry bots guarding the hangar which can be taken out with emp grenades or you can sneak into the two security rooms and shut them down. Either path will still give you the smooth operator bonus.
Now a few words on your set-up.
Travel light. By this I mean settle on two weapons at the start of the game. One should be the stun gun. It is the smallest non lethal weapon and makes next to no noise. We also don't want to use it that much. It is for emergencies only. The more you focus on getting around the guards and alarms the better off you will be. Secondly, choose your lethal weapon for the first boss. Why only the first boss? The Praxis points that should be invested at the beginning of the game are not going to go into adding more inventory room. By the time you reach the second it is possible to add more room, however it is one of the last priorities. Any weapon or ammo you pick up at the beginning should be immediately sold for credits. Credits should be spent on praxis points first upgrades second. Any gun you could want can be found and since I am focusing this around not doing sidequests, the praxis points will become even more valuable.
My choice of lethal weapon up until the first encounter would be the combat rifle. And to tell you the truth it is the best weapon in the game. Crazy as it sounds, you cannot beat it's all around effectiveness. It fires fast and reloads fast and has very little recoil. The target seeking upgrade, silencer and laser target system also make it just that much better. I suggest that whatever upgrades you find or purchase should be dumped into it to make at the very least the first boss fight easier, but you are free to choose whatever fits you better.
I stated before that mines will come in handy. Mines > grenades. You can toss the grenades and it could possibly land no where near your target, which hopefully is only the bosses. The mines will make up for the lack of a power weapon in your inventory and will leave more space for other things. Gas grenades are unnecessary as are emp grendades as obviously, the point is to avoid conflict as much as possible.
The reason I am suggesting to travel light is mainly so that you can stock up on Cryto bars and mines. Cryto bars will give you back energy cells and the mines will help with taking out the bosses. Since 3/4 bosses literally chase after you, you can lay the mines down in their path and make life that much easier. It also saves room instead of carrying the grenade launcher or the rocket launcher.
The other reason is for what you are investing your Praxis points in to. What I believe to be the most necessary for stealth I will list in order of importance.
1. Lift/move heavy objects. I think most would say cloak should be the first that you get, but it honestly is this one. So many vents and air ducts are covered by heavy objects this one should be a no brainer. On my first play-through I didn't activate this one until halfway through the game and after activating it and finding out how much easier it was to navigate the areas with access to all the ducts this one went straight to the top of my list.
2. Cloak. If they can't see you they can't be alarmed. Also cameras and turrets can't track your invisibility as well as giving you the ability to walk through wall lasers without being detected. The guards can still hear your footsteps, but you should be moving slowly anyway. This achievement is going to take patience, lots of patience. Cloak does not work on mines....found that one out the hard way.
3. Hacking Level Increase/Stealth. Level increase and stealth should be alternated that way your risk of detection is lessened as you play. Also, being able to hack higher security levels will give you opportunities to shut alarms down and open new paths once you activate the domination nodes.
4. Cybernetic Legs. Being able to jump a little higher seems pointless at first, but there are many areas where that little extra leap will get you above security systems and guards. Not all areas have boxes to stack or they are too out in the open.
5. Icarus Landing System. Once you are able to access higher areas to get around guards you are going to need the ability to fall from any height, plus the animation looks killer.
6. Punch Through Walls. Another one that will open up new paths and get you around security systems and guards. It is far down the list because of the noise it creates.
7. Energy Cell Recharge Upgrade. Quicker energy recharge will help you move faster since you will have more energy for your "power" moves.
8. Extra Energy Cell. Why is this one so far down and after recharge? Because no matter how many of these you have only the very first one will recharge anyway. In my playthrough I basically did the last 10 hours with only one energy cell. It might slow you down more, but bee lining it will get you noticed as your footsteps will be heard so consider waiting on this one as constraining yourself and helping you to slow down.
9. Dermal Armor. I didn't start upgrading this until halfway through the first playthrough and I was doing fine. Any areas that there is electricity on the ground you can usually stack boxes to get across it. It is helpful eventually.
10. Combat Reflex. Taking down 2 soldiers at once is awesome no one will deny that, but it is truly only necessary later on in the game when more and more soldiers are grouped together.
The rest of the augmentations are either useless or are nice to have, but not as necessary as the ten I have put above. Walking silently is a waste of a point as going invisible and walking slowly is much more useful. Landing silently is nice to have, but there are very few areas where you can call it useful. If by some chance you do have extra points to spend invest in the Typhoon System as it will help you with the bosses although you should be able to make it up by carrying mines with you. Being able to see through walls is another one that is nice, but is not necessary. Most of the guards move around anyways and you can use cloak to quickly look around walls and retreat. Expanding your radar is another nice one, however rarely did I find it truly useful as the standard radar is usually good enough and sneaking around will get you close enough to pick up enemies on.
The whole point of this set-up is to make sure you are unseen and giving you the best chance of avoiding the security systems and guards all together. Taking less risk means not running up and knocking out every guard you see. It doesn't mean it can't be done, it can, however make it easier on yourself by just getting around them and focusing on not setting off alarms and getting to the endgame.
Find the eBooks. I know I said to focus solely on Foxiest, but most of the eBooks are usually right by you and since there are 29 of them at 200xp a piece that is enough experience for a Praxis point and then some. This is a good way to get some extra points and for the most part they are in areas that are in city hubs out of mission or in secure places for you to take refuge in.
Hopefully I have answered any questions that anyone might have. I plan to use all I have said when I go through on hard mode. I know it's not a solid solution, but I hope that you find some good tips in there or at least something to lead you down the right path. Any questions you have just leave them in the comments section. Happy Hunting!!