Beat the NEW CHALLENGER mode, DEFENDER mode and CHAMPION mode. And you will unlock extra characters and an arena select.
Fight as Bumblebee Man
Play the NEW CHALLENGER mode and beat the Bumblebee Man. Save the game and look at the character selection screen.
Fight as Moe Sizlak (the bartender)
Play the DEFENDER mode and beat Moe. Save the game and see if Moe is selectable.
Fight as Ned Flanders
Play the CHAMPION mode and beat Flanders. Then do the same as above.
Fight as Professor Frink
Plat the CHAMPION mode and beat Frink. Then do the same as above.