Unlock the following costumes by performing the corresponding tasks:

COSTUME - HOW TO UNLOCK
Baby Crash costume - Collect all Die-O-Ramas
Evil Crash costume - Find Cortex on Mystery Island, and behind him should be an owl-shaped lamp. Use the body-slam switch to raise the lamp, then enter the revealed cave and go to the right. Talk to the drone at the top of the small island to purchase the Evil Crash costume for 2,000 Coins.
Skeleton Crash costume - Talk to the Astro Land worker near the stunt arena to purchase the Skeleton Crash costume for 4,000 Coins.

To easily get coins, drink a Whumpa Whip and let a Ninjua Penguin attack you. Then, pick up the coins.

Unlock the following tier of kart weapons for purchase by performing the corresponding tasks:

WEAPON TIER - HOW TO UNLOCK
Second tier kart weapons - Spend 500 coins at Midway to buy the following character's second tier kart weapon from them: Coco, Crash, Crunch, N. Cortex, N. Gin, Nina, Pasadena, and Von Clutch.
Third tier kart weapons - Spend one Power Crystal at Midway to buy the following character's third tier kart weapon from them: Coco, Crash, Crunch, N. Cortex, N. Gin, Nina, Pasadena, and Von Clutch.

Unlock the following characters by performing the corresponding tasks:

CHARACTER - HOW TO UNLOCK
Crunch Bandicoot - Give Crunch Bandicoot 2,500 Coins at Midway
N. Gin - Give N. Gin the Green Plutonium at Midway
Nina Cortex - Give Nina Cortex the keys at Midway
Pasadena Opossum - Give Pasadena Opossum one Power Crystal at Midway
Von Clutch - Give Von Clutch one Power Crystal at Midway