Are there color passwords for sonic battle

no. you either earn them or use a gameshark.
the passwords are for "*character name* combo" moves. they're all the same thing: they use the 3 basic attacks of their significant character, and then finish with a stronger attack, varying which character. for example, Sonic combo finishes with a shot attack, while Shadow's finishes with the basic heavy attack (Chaos Nightmare)


as far as colors go, though, there are no passwords. passwords are only for combos =(