After you defeat the Czar Dragon and Zombone, the Axem Rangers steal the Star Piece, and you catch up to them.
Defeat the Axem Rangers
Defeat Axem Pink first, since she can heal the other rangers. Then defeat Axem Green since he can do magic attacks, such as Solidify. Then defeat Axem Black, since he often does multiple attacks per turn. After that, defeat Axem Yellow, and leave Axem Red for last.
After you defeat all five, they will hop into the vehicle, which hits all characters with Breaker Beam, a high-damage attack, then recharges on the next turn.
After the battle, there will be a cutscene, and you will get the red Star Piece.
For an optional reward, go back to Nimbus Land and go into the castle. Keep going northeast until you reach the hallway with three doors. Go through the door that has guards next to it, then go northeast from the room with the statues of Mallow and the others, then go northeast from the room that has a ledge overlooking the lower part of the room. Then go northwest into the room where a prisoner gave you a key. Talk to the people there, and you will get a Flower Jar.
Before you can proceed to the next area, you have to visit the king and queen, so exit the room where you got the Flower Jar and keep going northeast. There will be a cutscene in the throne room. Go through the north door after the cutscene, and go northeast. If you didn't hit the chest in the hallway when you went through here before, you can hit it now to get a Flower. Then keep going northeast, and when you're outside, fall down until you are back at the entrance to the hot spring. Jump on the smiley springs to get back into Nimbus Land, then go northwest to the next screen. Talk to the guard, and the Royal Bus will take you to Bowser's Keep.