The third floor was the library.
Because libraries played the role of providing important backstory in every ancient city, they had put a great deal of effort into building the third floor. It also contained quite a few mechanisms and secret chambers. If even one secret chamber was left unopened, the plot would not flow smoothly.
Tim's premonition had been correct. The floor's basic structure and decorations, assembled by Arkham Asylum's criminals, had no problems whatsoever. But the various mechanisms put together by these amateurs were riddled with issues.
To create a sense of danger, a Chandelier was supposed to crash down in the corridor after they opened the mechanism door.
The mechanism was controlled by a timer. Batman was meant to step on a pressure plate, and three seconds later the Chandelier would fall, landing right in front of him.
But the timer's pressure plate had been installed a little too tightly. Batman was not heavy enough, so it did not trigger when he stepped on it. Superman, walking behind him, weighed more and triggered it immediately when he stepped on it.
That made the Chandelier fall later than intended, and it came straight down at Batman's head. Superman and Wonder Woman did not know the mechanism's exact details. By the time they reacted, there was only a bang, and Batman had been smashed flat.
He crawled out from a pile of shattered Chandelier pieces, clutching his head and sucking in a sharp breath. Superman and Wonder Woman hurried over to help him up, while Batman said, "Damn those crafty cultists!"
Tim looked down through the hole the Chandelier had fallen through. Fortunately, he had reacted quickly enough to tug on it as it fell, keeping it from dropping straight down. Otherwise, Batman might already have been in pieces.