Prince Bully is like a normal Bully but he is clad in armor. He chucks fireballs and charges you, which is his downfall. Wait for him to charge you then knock him into a clear pipe. He’ll come back around as a tin can, vulnerable to a jump attack at this point. He’ll bounce around the room and recover, repeating the cycle two more times.
Grab the Green Star once you’ve defeated him then head to the next level.