To unlock the Black Bomb (it’s an upgrade for the Green Bomb), eat five blue ghosts in Pac-Mobile mode.
To play as Fygar from Dig Dug, you have to win the circuit races and rally under the hard difficulty setting.
To play as Pooka from Dig Dug, win the circuit races and rally under the normal difficulty setting.
To play as The Prince from Katamari Damacy, try to win the circuit races and rally under the easy difficulty setting.
The last tip I would propose to you is how to unlock Nightmare Difficulty Setting. You have to complete the Rally Cup on Hard difficulty. That’s it!