Play As Devil Kazuya:
To play as Devil Kazuya you must beat all the rounds of Galaxian at the beginning of the game.
Play As Heihachi:
To play as Heihachi you must beat the entire game without continuing.
Play As Sub-Boss:
First beat all the normal characters in the game. After beating all the characters you will have to fight your character's sub-boss. After beating that sub-boss you will be able to play it as a normal character
Play Galaga With Two Ships:
During power-up, press and hold Up+L1+Triangle+X on the player two controller.
Play Galaga continuously:
Press select after it shows you the kill number and you should hear a "ding" noise. Instead of skipping to the intro Tekken screen, it will go back to the same Galaga level you were on.
Thanks to Revolution reader Zach White, David Mears, and Cyrus Maxim!