In Ape Escape 2, Red Monkey's boss battle includes him casually beating up a dinosaur as one of his attacks.
The protagonists of all three main games should definitely qualify for one of these, if just for the sheer absurdity of their situation. Within the first few levels of 3, you will crash a Monkey Wedding, fight a Robot Dragon, fight a monkey with a chainsaw and battle another monkey using Humongous Mecha.
The battle with Doctor Tomoki has you pit your mecha against his.
Specter's plan in '3''. Chop the Earth in half. You just don't see insanity like this any more.