This solution is based somewhat on Maka's suggested route and other tips I've read around, including some adaptation from myself. I did this on Survival since it made sense at the moment to leave the combat for Spartan and stealth for Survival. I had no idea the modes altered the levels and guard behaviours, etc. So, I also found myself confused and trapped following Maka's guide.
Note: I did manage to get the achievement while having loaded the checkpoint multiple times, from either alarming the guards or killing them and reloading (second is because of vinegar.) So don't worry about having to do this from the beginning cause you don't.
Here is what I did:
1. Let the first 2 guards make their way to the dead end. You can choose to knock them out but I just let them be.
2. As you are approaching the left side with the boxes, make sure you shoot that light bulb below the boxes. This is critical.
3. After you kill the light, approach while crouching, reaching all the way until you're facing the door you are supposed to go through but at the same time with your back at the wall. You should be getting a checkpoint as well, at this point.While you are waiting for the crane operator to stop, you can choose to shoot the horizontal light bar that is located on the far side of the room. You can get a shot at it through the fence.
4. After the crane operator drops down and turns his back, you can start creeping up behind him, not too close though. Make sure you turn off the light outside the main room, you can do this while still crouched. After the light is off you can enter the room but make sure you are hugging the left side at all times and always look at your watch to make sure you're not visible. (although if you are, you will know cause they will start shooting at you) Don't take too much time, as the guards who were sitting on the main room will start walking around soon.
5. That's the tricky part. The crane operator will go in the main room and then take an immediate left through another door. This is where you have to be swift. There is a light bulb and if you expose yourself too much, you will fail. Let the operator take a few steps, then go through the door quickly while crouching, favouring the left side and as you exit the room, knock him down. Try to knock the crane operator OUTSIDE the second room, if you do it inside, his friends will notice him and will be alarmed.
6. Afterwards, you want to reach for the stairs, still crouching and cautious. You should now be reaching the light source you were supposed to disable in step 3. If you haven't done so, you should still be able to do it then, although I have not confirmed it.
7. There is one final staircase and one final light bulb above the door. Shoot it off, no one should notice and you will have a clear pass to the door.
8. After you're inside, you will be faced with the surrendering guard. I just chose to knock him out cause I didn't want to risk anything, like him screaming or attacking from behind. Enter the vent, the mission should end there and the achievement should pop while you're in the black screen.
Like I said, this solution is based on personal experience as well as tips and other solutions, like Maka's. It might be too detailed, it might not work or it might just be what you need.. Nonetheless, I wish you good luck with it.