I think you can get Adamantine from one of the Brothers Card, Minotaur.
As for leveling up, I remember when I got stuck with the first battle with Rajin and Fujin and ,yes, forgot to draw out Leviathan. The first time I played this game I totally sucked. But then after playing about five times and finding myself getting nowhere, I decided to level up to Lv100 since leveling up is so easy. Then finally after learning my lesson that drawing and junctioning magic AND getting as much GF's as possible is so important, I finally beat the game in peace (took me alot of times to get it right, though)...... Now I find myself playing it all the time!
Having your characters on Lv100 is well worth the hours, hours, and hours of leveing up.........OH, and their strength is very IMPORTANT!
Its a good idea to have a character with the Str Bonus. I junctioned it to Rinoa and by the end of the game her Str was 238!
Well, I better shut up now because I'm typing too much........Good Luck!