There are three Dog Tag Challenges. The Bronze Dog Tag Challenge is unlocked by beating the main game once. The Silver Dog Tag Challenge by beating the Bronze, and the Gold Dog Tag Challenge by beating the Silver.
X2: Wolverine's Revenge [Xbox] Master code:
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.