I just did a lot of time in the Battle Arena, so i've gotten together some decent srategies and tips from my own experience. Here's what's worked for me:

- Equip whoever's fighting with a Mystile armlet (for the high Evasion and Magic Evasion), and a Ribbon, and the best weapon they've got. Ultimates work best, as long as they're powered up.

-If you're not wearing a Ribbon, DO NOT try to escape status ailments by using a Vaccine or casting Resist. The ailments that the slots give you will still be in place, and you won't be able to cure yourself by any method. So, if you roll Toad on the reels, you're stuck as a toad for the rest of the battle, no matter what you try to do.

-Equip your best Materia, but don't make your character dependent on them, as one way to gain the best BP is to roll All Materia Broken. More Counter Attack Materia is great, because then you'll strike once for every Counter Attack you have equipped, and you can use your turn to heal yourself rather than fight.

-If you ARE wearing a Ribbon, roll Toad, Minimum, and Poison as much as you can; they're great as far as BP goes, and you won't be affected by them. These aren't even that bad if you're not wearing a Ribbon, as long as you've got the appropriate remedy items or magic.

and, this last one may seem random, but...

-If you should end up fighting a Ghost Ship, KILL IT AS FAST AS YOU CAN!!! Ghost Ships have a move called Goannai that ejects you from battle, meaning you lose all your BP and you can't do anything about it. They use it once they get low on HP. Casting Berserk on it or using an item to do that will make it only attack physically; it'll do more damage, but you'll get to keep your BP for sure.