Get all ten Lightning Cards from the evil bombers, then defeat the Boss in level 5-4 (Warhorse). The Planet Bomber world will now be unlocked. In it, you will battle two new Bosses (Mujoe and Dr. Mechadoc).
Bomber Mansion
Start a new game as bomberman, then kill yourself with bombs. The Prof will say you need more time at Bomber Mansion. When it asks you to continue, select no and go to the main menu.
