Another World:

At the “Press Start” screen, press Triangle, Right, Left, Triangle. If you

did this correctly, a icon will appear in the top right hand corner of screen.

Unlock More Stages:

When the Push Start screen shows up, press: Triangle, Left, Right, Triangle

A small icon will show up in the upper right hand corner saying that you have

unlocked new stages. The extra stages are in Puzzle mode.

Unlock More Characters:

When the Push Start Screen shows up press: Triangle, Right, Left, Triangle

An icon will show up in the upper left hand corner of the screen saying that

you have unlocked new characters.

Thanks to Revolution readers mystic_gohan and teie!