Play as Mr. Karate
Beat the game with everybody and win without losing at least once to get Mr Karate.

Play as Duck King/Bonus Modes
Beat the game with Mr. Karate, Duck King will appear on the left side of the question mark meaning he is playable. Also after doing that, the team battle mode option and data mode will appear.

Geese's Hidden Costume
At the Character Select screen, highlight Geese. Hold the START button, and press circle or X to play as Geese in his black suit (square and triangle will give you Geese in a dark brown suit).

Geese Ending 2
To get Geese's 2nd Ending, you must beat the game with Geese wearing one of his suits. The only difference between his 1st ending and his 2nd, besides the fact that he's wearing a suit is that Geese doesn't smile after walking away.

Billy's Ending 2
To get Billy's 2nd Ending, beat the game with Billy wearing his other costume.