Go to the "Cheat Code Screen" in the "Options menu"
and enter the following cheat to unlock: 

Note: If done correctly, the code will appear in the
box to the right.

Unlimited Ammo
Down, X, Left, Circle, Down, X, Left, Circle. Press 
START to confirm code. 

Invincibility
Left, Square, Up, Triangle, Right, Circle, Down, X. 
Press START to confirm code. 
  
Unlock Invisibility
Left, Square, Right, Circle, Left, Square, Right, 
Circle. Press START to confirm code.

Unlock Slow Motion Mode
Right, Square, Up, Triangle, Right, Square, Up, Triangle.
Press START to confirm code.

Unlock Xen Gravity
Up, Triangle, Down, X, Up, Triangle, Down, X. Press 
START to confirm code. 

Unlock Alien Mode
Up, Triangle, Up, Triangle, Up, Triangle, Up, Ttiangle.
Press START to confirm code.