Meat Circus

The Meat Circus was created through a blend of Razputin and Coach Oleander's childhood memories. Raz was brought up at a circus where his father was an acrobat, and Coach Oleander's father was a butcher, leading to the creation of a literal circus made of meat. Since it's a melding of two people's subconscious, it often uses their fears against them, such as through rabbits falling into giant meat grinding machines and water rising when Raz is cursed to die in water.  It is essentially a nightmare circus.
 
Here, Raz fights both his own depiction of his father and Oleander's depiction of his own father, as well as a version with them both melded into one. 
When Raz and Coach Oleander's minds separate, the Meat Circus ceases to exist as the memories disentangle themselves.
 
It is also notable for being the only location in the game that Raz cannot return to the real world from without completing the level, allowing for a stall to be located where Raz can redeem psi cards and cobwebs in lieu of using Agent Cruller's machines.  
 
This level is known to be extremely frustrating: Double Fine have admitted that they ran out of time to sufficiently playtest this level.
Gameplay videos are available for the more unbalanced parts:
Butcher Boss (1) | Escort Little Oly | Big Top/ Acrobat Run | Butcher Boss (2)