To get Billy's 2nd Ending, beat the game with Billy wearing his other costume.
Bonus Modes
Beat the game with all of the characters including 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. Note: always save your game so no data will be lost.
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.
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).
Play as Duck King
Beat the game with every character.
Play as Mr. Karate
Beat the game without using any continues or losing any rounds.
Team Battle
Complete Arcade Mode Using All Starter Characters.