Woot! I finally kicked Minerva's butt (Hard). That was tough, about 2 hrs to get through *Phew*. To me the biggest threat was always Fast slash, since not guarding it would 1-hit-kill me (that's how she got me on 95% of my unsuccessful tries). Anyway, I personally went with Costly Punch, Wall, Curaga, Mug (to get all the Phoenix downs) and Regen - that last item is quite different from most people's build, but I personally liked having a steady stream of HP to offset a portion of the HP costs from Costly Punch. Maxing HP, VIT, SPR seemed a requirement. Also, I took great care of saving limits to interrupt Minerva's Ultimas as often as possible. In the end, all the phoenix downs I used were because of Judgement arrow and Fast Slash, which both remove re-raise - I did not use a single one for its intended purpose!
Once she got into her final attack pattern, below 23 Millions HP, the fight really became a slug-fest because I only attacked after she used her weaker spells (Thor's hammer, Krista and Crimson Flame) - otherwise I'd get punished with Fast Slash if I got greedy or careless. It required a lot of patience!