I've beaten her, after being owned too many times. I think I went through about 30 odd Phoenix Downs in that battle.
My strategy, if you call it that were continously keeping the Phoenix status, dodging all but that ice attack while using Costly Punch. However a limit break ruined that move for me, luckily Minerva likes to kill me a lot so the HP break issue with Costly Punch isn't much of an issue. Also you have to have a huge amount of HP or that move that removes your Phoenix status will obviously finish the battle for you.
Does anyone know how you dodge that ice move, I roll at several different times, I've tried blocking.. she hits you 99,999 damage no matter what. I could dodge everything else but that special move she does.