Make sure that you do NOT go back to bed during Day Two, otherwise you will not be able to obtain this achievement.
Head to the Facility and pretty soon the power will go out. Head to the Generator, it is to the right of the entrance to the Apartments. Go inside the hut and interact with the Generator to rewire it. Once that is done, finish your day and head to your Apartment and sleep. When you wake up, you will notice a red light. Use the fire extinguisher (from the Ground Level Kitchen) to bash the door open. Grab the Safe Key from the wall. Now go up to Floor Four, Room Four and take the Key Card. Head to the Facility and go to the Fourth Floor and all the way left to the safe. Interact with the Safe and you will automatically use the safe key. Enter the code 1972. The Safe will open and you will get the other Key Card. Head to the Ground Floor and use the second elevator to go to the Lower Levels. Head all the way to the left and enter the freezer. You will find Buck frozen and dead, the achievement will immediately unlock upon entering the room.
Note: If he does not appear the first time, exit and re-enter the room.