You can unlock achievements in special rooms like this by performing specific actions or fulfilling certain conditions. These rooms are always out of the way of the red wires so you’ll have to stray off the path and rely on visual clues to know where you are.
The hallway that leads to the gymnasium is in the lower floor with the upside tables, (with a single book that will fly away once you walk by). You’ll see some long benches on the side of the hallway.


