In order to unlock this, you need to solve the mystery. The mystery is solved by
1st Segment*** Spoiler - click to reveal ***For the 1st segment, you need to guide Wayne De Spiritwhistle and Patrick Bannon through the rooms in a specific order:
First you send them to The Sound Stage (button with the megaphone)
Next you send the duo over to The Prop Store (button with the dumbbell)
Lastly you send the two to The Costume Room (button with the hanger)
(Note that this is the path I took. Judging by the end screen, the only thing that matters might be the last step)
2nd Segment*** Spoiler - click to reveal ***For the 2nd segment you need to sacrifice both Holly and Patrick at certain times.
The very first sacrifice will be Holly. By sacrificing her first, you make her go to The Sound Stage and later The Vault.
The 2nd and 3rd sacrifices don't matter as long as neither of them are Patrick, as you need to keep him safe until the end. This will make him go to The Projector Room.
3rd Segment*** Spoiler - click to reveal ***As long as you sacrificed Holly first in the last segment, she will find herself in The Vault. At this point, there is nothing special that you need to do.
Going for this achievement will also unlock both A Fall From Grace? and A Burning Question achievements on the way.