Do the "another world" code at the title screen (L, up, R, down) then instead of going to the puzzle mode, go to player vs. player. Once you get there you can choose your character. Depending on how far you have gotten in player vs. computer, more characters will be available. If you beat the whole game then you can choose everyone.
While playing a level, press Z, L, R, and A at the same time to skip to the next stage.
Hidden Characters (Puzzle Mode)
At the Puzzle Mode screen (were you select A or B) press Left, Left, Up, Down, L, R, L, R, and then L&R at the same time. This will bring up a character select screen, in which you can select either color dino, or one of the bosses. Be sure to press each button slowly -- don't go too fast.
Another Puzzle World
At the main menu screen that reads, "Game Start", Time Attack", and "Options", enter the following code: L-Button, up on D-pad, R-Button, and down on D-pad. This will give you access to "another world" full of new puzzles. After inputting the code, a tiny character will appear in the lower right portion of the screen. Select "game start" and when you select "Puzzle Game", it will say another world underneath it. Press A and you'll go to another world!