To play as one of the following character, you should do the following:
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
Baby Crash costume: collect all the Die-O-Ramas