Challenge Mode
In order to unlock this mode, you need to beat the Story Mode.
Extra Characters
In order to unlock these characters for play in the several modes available in the game, perform the task stated after it:
Penny - Beat level "Try, Try Again" of the Story Mode, and then buy her for 140 nuts.
Stella - Beat level "Depelter Turbo" of the Story Mode, and then buy her for 70 nuts.
Extra Cups
In order to unlock Backyard Cup, which you can play in the Arcade Mode, beat "FANtastic" in the Story Mode and then buy for 210 nuts.
Sound Test
In order to unlock the Sound Test option, you need to beat the "Ozzie's Trek" level of the Story Mode.