Level select:
Press Triangle, Triangle, Triangle, Square, Square, Circle, Square, Triangle, Circle, Square, Triangle, Square, Triangle, Square, Triangle, Circle, Triangle, Triangle at the title screen. Then while playing, press pause and access the cheat at the level selection screen.
Invincibility:
Press Triangle, Square, Square, Circle, Circle, Circle, Triangle, Triangle, Square, Square, Square, Circle, Circle, Circle, Circle, Square, Triangle, Circle, Circle, Circle, Square, Circle, Triangle, Circle, Circle, Square, Circle, Circle, Triangle, Circle, Square, Circle, Circle, Circle, Triangle at the title screen. Then while playing, press pause and access the cheat at the level selection screen.
Credits:
Press Triangle, Square, Circle, Triangle, Triangle, Square, Circle, Triangle, Square, Circle, Triangle, Square, Square, Circle, Triangle, Square, Circle, Triangle, Square, Circle, Circle, Triangle, Square, Circle at the title screen. Then while playing, press pause and access the cheat at the level selection screen.
Secret level:
Press Triangle, Square, Circle, Circle, Square, Triangle, Triangle, Square, Circle, Circle, Square, Triangle, Triangle, Circle, Square, Triangle, Square, Circle, Circle, Square, Triangle at the title screen. Then while playing, press pause and access the cheat at the level selection screen.
How to beat the swiftly-flowing water in The Sewer:
When in the first press down the D-pad or L-thumbstick and forward at the same time. When you've passed through them there's another one that's going down, so this when you go down you have to extra quick, press up the D-pad or L-thumbstick and forward.
(supplied by: Swedish Gamer)