Monkey is a colossus that, for unknown reasons, did not make it into the final version of the game. It is one of two unused colossi, the other being Sirius, that doesn't have a different name given by fans, it's therefore called Monkey as the designers nicknamed it.
The artbook says, 'It hung from the ceiling, and you'd defeat it by dropping it to the floor'. That, coupled with early sketch designs, indicate that Monkey was fought in a cave-like area where it would hang on to stalactites. It is likely that Monkey would either attack the player by letting stalactites fall, or by dropping itself on the player. There is also the possibility, that Wander had to shoot the stalactites Monkey was hanging on to make it drop.
In the screenshot of Monkey, it's shown hanging using its two limbs. In early sketches, the colossus is seen holding on to stalactites with one, two and four limb(s).