Walk Through Walls:

At the main menu hold R2 + L1 + Circle + Square and press Select.

Invincibility:

Press Start to pause game play, then hold R2 + L1 + Circle + Square and press Select. Select the "Cheats" option to access an option for unlimited lives.

Level Select:

At the main menu, highlight 'New Game'. Press and hold L1 + R2 + Circle + Square + select. Highlight 'New Game' and press Right to select your level. Press X to go to the level you've selected.

Hints

Save Continues:

I found that when you save a game you also save how many continues you have. When you get to a save point in the game and are almost dead the best thing is to save the game where you are press start, exit the game, then reload your game you start right where you saved it last but with full health so you can hopefully make it to the next save point without losing a continue.