Prince Bully is a silver-clad leader of all Bullies, and unlike those guys, you don’t have an easy way to knock him off a ledge. What you must do is force him into one of the nearby Clear Pipes. He can do more than just ram you; Prince Bully can also spit fireballs at you!
After you have shoved Prince Bully into a pipe, he pops out on the other side of the room, tightly compacted. Stomp on him then to score a hit! He’ll bounce around the room before recovering. He can take only three hits before he’s defeated, and he gives up a Green Star for your trouble.