As soon as the level begins, spikes will start falling from the sky. They look dangerous, but they don't hurt you, so just relax until the robo-collector comes along. When it reaches out to collect the first of the townsfolk, you can start hitting it, so get under it and just start hitting up at it like crazy. You have plenty of time while it picks up everyone and slowly makes its way out of the screen. (You don't have to destroy it, but there's a Secret Bonus Point in it if you do!)
Anyway, after that, the Yellow Baron will start firing at you, but if you just go to the right end of the screen, you'll avoid all the projectiles. Then, you stop, and the wall collapses on you (no health lost), revealing Trouble Bruin in the background, who jumps forward to the right side of the screen. He'll begin sucking in energy balls from all around, so get to the left side of the screen and stay there until he stops. This way, none of the energy balls will touch you. Then he'll jump in the air four times, and charge towards you. Jump over him, and as soon as he hits the wall, run back under him so he flies over you. Energy balls will start coming out of him, and you should be able to see gaps between each one, so walk to the furthest one possible. Keep dodging under and over the energy balls until you can see that Trouble Bruin is tired, meaning you can now hit him, but be quick. Repeat the whole process again, and he'll be defeated on the second hit.