There are three Combat levels:
1. The rematch against Tess's giant insectoid robot follows the same basic rules as the main game. The floor is now made up of relatively slow-moving treadmills moving towards the center, making it a little harder to get the switches on the outside edges, but I had a lot of success jumping to the edge and attacking on my way down. There appear to be more lasers than last time, too, but nothing too terrible. Just keep half an eye on the laser movement pattern, and you'll be fine.
2. The rematch against General Buttons and Fluffinstuff, again, follows the same basic rules as before. Beware, though: when they fire the bombs, you don't have much time to figure out which one to send back. The ones you don't WILL DESTROY THE PLATFORMS THEY'RE ON. Be strategic! I recommend keeping a consolidated area available of at least 2x2 platforms if possible, for ease of movement when dodging the fireballs. Beyond that, just smack a bomb at their ship again 3 times, and you're done.
3. "WriggleMania" is a relatively simple set of 4 waves of enemies. Each wave gets a little harder (adding fireballs and such), but still not that hard overall. I recommend staying off the floor when you can. As soon as the enemies appear, jump up and bounce on one enemy's head, then double-jump off of them. Each time you land on an enemy, you get your second jump back. So when you can, do that to eliminate as many of the enemies as you can right off the bat. I found it easier to target long-range ones like bees first, to make things simpler.