On the options menu, highlight the "Training mode" selection and press L1 + L2 + R1 + R2. Now additional options, including invincibility and stage skip, will appear.
One hundred lives
At the title screen, press Up(2), Down, Left, Right, Down.
Same character game
Start a two player game. Then, press Start, Select, choose a new character and press X. While the new character appears in the blue ray, quickly press Start, Select on the other controller. Now both players should be playing the same character.
Stage select
Enable the "Hidden options" code and activate the stage skip option. Then while play a game, press L1 + L2 + R1 + R2 to display the stage select menu. Press Up or Down and press Triangle or X to select a new stage. Then, press Start to continue the game at the selected stage.