To get this achievement, you must first locate one of the seven VHS tapes. (See the "Dwayne's memento master" achievement.) Put it into the VHS player to the left of the TV in the living room(not the basement), and the TV will play a short video clip on repeat.
The video clip gives hints to where in the house you must go and what you must do to start the chosen storyline. Each VHS has its own storyline with new areas to play through. At the end of each you will find a small piece of blank metal - a piece of the Mirror Mask.
Obtain any one of these pieces, and the achievement will pop!
Note: The easiest/quickest one to get is probably the Addiction storyline. Play the Addiction VHS, then go to the master bedroom. Where the bed was, you'll see a hole. Go down. Interact with the bed sheet where it seems like someone is sleeping. Go to the TV and sit down. Take a drink every time you're prompted to. At the end you'll get your Mirror Mask piece!