Unlockable: Characters
Fygar - You must complete Rally Cup on Hard Difficulty.
Pooka - You must complete 'Rally Cup' on Normal Difficulty.
The Prince - You must complete Rally Cup on Easy.
Unlockables: Tracks
Easy Classic Cup - You must obtain a Gold Medal in Easy Watermelon Cup
Easy Rally Cup - You must obtain a Gold Medal in Easy Classic Cup
Easy Watermelon Cup - You must obtain a Gold Medal in Cherry Cup and Grapy Cup
Unlockable: Nightmare Difficulty
Beat all the cups on Hard Mode with a gold trophy.
Source? Here it is.