Complete the indicated areas to unlock the corresponding costume.

Costume	How to unlock
Magmaden costume	Junkyard Arena. Take the "Roller" exit with all the Mojo to go to the far side the village and talk to the cub for the costume.
Ratcicle costume	Ratcicle Kingdom Arena. Talk to the character on the right for the costume.
Skeleton costume	Mount Grimly Arena. Go to the area where you first encountered Yuktopus and talk to Uka Uka for the costume.
Snipe costume	Wumpa Island Arena. Talk to Crunch for the costume.
Spike costume	Desert Arena. Talk to the three headed mutant for the costume.