Kao the Kangaroo

Story-related; cannot be missed.

Jayabaya is the boss of the second area, and while he's quite big and you do much less damage to him that the first boss, he's pretty easy.

In the first phase, he's pretty aggressive, but you can do the same. He'll jump at you, so just roll away out of the circle, then roll right back in and start punching. When he winds up to hit you, roll behind him and keep the combos going, even through his next attack, until he jumps again. 

For the second phase, he'll be up on a ledge and will throw mugs at you. You'll need to jump and hit them to deflect them back at him. Between each, you'll need to fight a simple mob of enemies. 

For the final phase, he comes back at you with all of his attacks. Just roll behind him and keep the combos going throughout. His quick ground pound doesn't seem to hit you if you're behind him, despite the circle on the ground indicating that it should hit you.