This is exactly the same achievement as "Going Dark", except that it's on a different level and harder that you think. However, it can be done. In fact, it took me two hours to replay the level, over and over again, until I finally nailed it. Here's are some tips for those that need help.
First off, your recommend weapon of choice should be the P99 Silencer. No other weapon will work here, because they are loud and will alert the guards and cause them to bring reinforcements, so that's not an option. With the P99 Silencer, you should be able to take them out quietly with head shots as long as they are away from each other.
Second, you need to be crouched and moving slowly. Rushing through the level, for this achievement, does you no good. That said, make sure you get a good idea of where everyone is and then start picking them off, one by one. Like I said before, make sure they are alone and not nearby any of the other guards. Some will remain ignorant and keep slamming away at the machines, making them easy targets. Others will move around in a circle, depending on the room.
Do not subdue any of them. I don't recommend it. If they are near you while that's happening, the alarm will be raised.
There is one location, near the beginning, that has a bomb on the wall that needs to be defused. Unless you are going for the secondary objectives, don't enter that room. Just kill the three guards that you see and move past them until you reach the next area.
Finally, above all else, be very patient with yourself. It's going to be frustrating a couple of times, especially when you think that nothing goes wrong, only for a shot to miss or something along those lines to happen and it messes everything up. Just keep your wits about you, be calm, and eventually, you'll make your way to the server room.
Once you entered the elevator that leads to the server room, the achievement should unlock right then and there. If you still have trouble with earning the achievement, I have attached a video below showing how to get it. Credit goes to RoosterTeeth for creating and showing this video to the public. It's an excellent guide. Or you could check out the guide above you and that's an excellent one too! Have fun and good luck!