When you have access to the vault, use the following codes:

Debug mode:
Square, Square, Diamond, Circle, X, X (press Select for Debug menu)

Level select:
Square, Circle, Circle, Triangle, X, X

One-liners:
Square, Triangle, X Star, Square, X (press Select for one-liners)

10 Lives:
Square, X, Circle, Circle, triangle, Square

1 Life:
Triangle, Circle, Star, Square, Square, X

Invincibility:
Square, Star, Triangle, Square, Triangle, Diamond

Play as Alfred:
Square, X, Triangle, Square, Star, Star

Play as Cuz:
Square, Diamond, Square, Square, Triangle, Diamond

Play as Rex:
Square, Star, Star, Square, Triangle, Triangle

GEX Video 1:
Circle, Triangle, Square, Star, Diamond, Star

GEX Video 2:
Diamond, Star, Square, X, Triangle, Circle

GEX Video 3:
X, Diamond, Star, Triangle, Triangle, Circle

All GEX Videos:
Star, X, X, Circle, Square, Triangle

Eight Hit Paws:
Square, Diamond, Triangle, Triangle, Star, Diamond