Quote Originally Posted by fire_of_avalon
I can't remember where I picked them (the Black Magic spheres) up, but probably from some boss battle earlier in the game.

I beat Sin just a few days ago, and I didn't have Ultima. I just Hasteaga'd my party, then defended until Sin drew me close enough to melee. Then I used Armor Break, used Tidus's Energy Rain Overdrive, used Holy, did Mental Break, used Lulu's Flare Fury Overdrive, smacked him around a bit more with Auron and Tidus, then called Bahamut and he was super toast. But both Auron and Tidus were hitting close to 9999 at that point, and I don't know whether or not you're leveled that high.
No not even close. Is there a good place to really train? Monster arena???