This achievement is unlocked in Chapter 5.
In this chapter, you'll need to distract the guards to leave the Psych ward. There are several ways to do this, but you'll need to at least start one specific way.
At the front of the cell blocks, in the area the guard does not patrol, you can enter a conversation with one of the inmates. He'll ask for sleeping pills in return for distracting the guards. The pills are in the pharmacy on the center set of shelves, along the back.
The pharmacy is guarded by one guard, who follows the same path -- enters the store room, leaves the store room through the same door, enters the pharmacy, circles around the right side of the shelves and stops at the desk in the back, continues the right circle and exits the pharmacy, enter the store room, repeat. To get the pills, enter sneak mode and wait for the guard to enter the pharmacy. Follow him in and follow the same right path, waiting for the guard to leave the desk to enter the back part of the pharmacy. Once the guard is heading for the store room, quick grab the goodies back here (including the sleeping pills), then sneak over to the door and hide between the door and the desk. Wait here for the guard to re-enter the pharmacy, then sneak out the exit as he head right.
Return to the patient and give him the pills and the achievement should unlock.
NOTE: If you overload the gas pipes in the boiler room by setting all the pressure values up on the pipes than activating the boiler OR if overload the electric system in the experiment room by flipping all four electrical levers than activating the machine, you can no longer get this achievement. Therein, make sure you do this achievement first.