For Odin, use a Lit3 spell on him as soon as you can. When he raises his sword he MUST be struck before he swings it or you'll die. If you don't have Lit3, don't even try. But if you do, one bolt should be enough.

Edit: pretty much all of the battles in this game require a certain level to be successful. Leviathan and Bahamut as well. I think the "no leveling challenge" is really, really hard here.