All Atomic Snowballs:
At the mode selection screen press X, X, X, White Button,Y, Start.

All Boosts Mode:
At the mode selection screen press, Y, Black Button, Black Button, Y, R, Start.

All Grappling Hooks:
At The mode selection screen press, Y, Y, L, Y, Y, White Button, Start.

All Invisible:
At the mode selection screen press, X, Y, X, R, Y, Y, Start.

All Random Locations:
At the mode selection screen press, Black Button, R, X, Y, Black Button, R, Start.

All Rooster Tails:
At the mode selection screen press, Black Button, R, L, White button, X, Start.

No Drones Mode:
At the mode selection screen press, X, X, Y, Y, White, Black, Start.

Expert Mode:
At the mode selection screen press, Y, X, Y, Y, X, Start.

Clone Mode:
After startup and before selecting a player, press White, L, L, Y, White, Y, Start.

No Power-Ups:
Mode After startup and before selecting a player, press X, X, Y, X, R, X, Start.

Super Boost Wheelie:
Mode After startup and before selecting a player, press Y, White, X, R, X, L, Start.

Thanks to Revolution readers Frosty and Ali!