You can erase your save data and start fresh. 


This makes it so you have to unlock all levels, characters, and outfits again. This will also reset all of your Stats to zero, so you might lose progress on Achievements / Trophies. However, if you previously disabled Achievements / Trophies by using the unlock everything cheat code, resetting your stats makes it possible to start earning Achievements / Trophies again.


Go to the Menu --> Stats, and press the big red button at the bottom. This will erase your save file.