Defeating Barnabus is not required, though you may want to loot the areas accessed by the upper two teleporters, at least.

From the walkthrough:
Quote
-Accessing Barnabus requires taking the teleporter on the northeast side of
the bottom of the room. Inside, you must navigate a platform maze to disable a
generator. See below for step-by-step directions.
1: leap across a series of falling platforms
2: climb the ladder
3: use the moving platform to access a lever that activates a teleporter
4: Drop down and take the teleporter
5: navigate several more moving platforms, then climb another ladder
6: time your next jump carefully - the next platform also sinks
7: jump from the sinking platform to another moving platform
8: jump up to another teleporter and step inside
9: hop down a series of platforms in the corners of the room
10: flip the lever
11: wait for a moving platform to emerge from by the door, then jump against
the wall and fall onto it. Good kitty.