This is the hardest achievement in this DLC, but it's not actually hard AT ALL. A couple side-notes:
If you alert anyone, immediately press and load last checkpoint.
It is HIGHLY recommended to use thermal vision during this segment by pressing .
In the third mission, 'Last Rites,' you will come to a dark underground area. The first set of enemies will include two men as you exit a door. Let them pass and then move up behind them. One will stop by a fire and the other will stop at the stairs. In the distance to the right you will see one other soldier. Let the one at the stairs go down the stairs and then stealth kill the one by the fire. Now shoot the one to the right as he is walking away. Now look down and kill the one at the table (there is also a secret here). Continue forward until you come to the next room.
In this room there are two enemies to the far left at a door, but you can just sneak past them. Keep to the right side of this area and go right past them and then further down the right side you will see a part of a railing that is missing along with a series of pipes you can walk across. Quickly move across these pipes and go around behind them. Turn around and watch the stairs that you just went past. You will see three soldiers walk up them and away from you. Once all three are gone, move forward down the pipes.
There are two enemies left until you are home free. Kill the one on the walkway above once he is to the far left first. Now kill the one below you at the fire. Once they are dead, you can run for it. Go up the stairs and move towards the objective marker. The achievement will unlock as soon as you drop down outside.