To fight Geese Howard, defeat every opponent in the one player mode without losing a round at any time. After Mr. Big, you will fight Geese.
Art of Fighting: Play as ? (Mr.Karate)
In the one player story mode, get up to ? (Mr.Karate) and lose the fight. Now start the game with 2 players and ? will be on the character select screen and you can pick him.
Art of Fighting: Play as Mr.Big
To play as Mr.Big, get up to Mr.Big in the one player story mode, then lose the fight against him. Now start a 2 player game after losing too him and Mr. Big will be a selectable character.