Unlock the Password Screen
When you start a new game, you will notice there is no obvious password screen anywhere to be found. To use passwords, you must first unlock the password menu: Press and hold the "Up" button on your PS2 D-pad. Holding the "Up" button, press "X" to reveal the password screen. From there, enter any of the numeric passwords you want to use.
Unlock Everything Else
While you could go through the long campaign mode to unlock everything in "Godzilla Unleashed," it is much easier to enter a password to unlock characters and such instead. To do just that, bring up the password screen and enter "204935" (without quotations). Once entered, every single unlockable (characters, maps, etc.) will be immediately available to you.
Reveal Move Lists
Just because you have unlocked everything doesn't mean that you are a master at the game--yet. You can get the upper hand on the other monsters, as well as learn how to play the game, by entering "411411" (without quotations). This code will show a list of each monster's moves underneath the heads-up display, letting you see how to pull off crippling special attacks.