Press X, L, X, L, X(2), L, R at the title screen. New options will be unlocked each time this code is enabled.
Level select and all challenges:
Press X, L, X, L, X, L(2), R at the main menu.
Press L, X, L, X(2), L, R at the main menu.
All Cerebro files and FMV sequences:
Press X, L, X, L, X(2), R, L at the main menu.
Enter the following at the main menu:
If done correctly, you will hear a tone. Now when you begin a game, there will be a 'Cheats' option on the pause screen. You can toggle Invincibility On/Off from there.