Stats

Here are Kuja's stats in battle and some help on how to beat him!

Kuja
Lv: 64
Hp: 42383
Mp: 9999
Atk: 82
Def: 41
Monster Type: human
Battle Location: panemonium (disc 3)
Attacks: Flare Star, Demi, Thundaga
Status Defense: Petrify; Zombie; Stop; Float; Doom; Venom; Death; Poison; Heat; Mini; Silence; Confuse; Sleep; Freeze; Trouble; Berserk; Regen; Vanish
Steal item: Ether, Caribini Mail, Light Robe Battle strategy:
Although he can't be defeated, Kuja can defeat you if you deplete his MP. Make sure you don't use spells which target MP or he'll unleash his Flare Star attack which will easily take out your party. Hack away at his HP and he'll eventually use Ultima which will take out everyone and end the battle.

Trance Kuja
Lvl: 76
HP: 55535
MP: 9999
Atk: 96
Def 47
Monster Type: Human/Flying
Battle location: Crystal World (disc 4)
Attack: Flare Star, Flare, Holy, Curaga, Reflect
Status defense: Petrify; Zombie; Stop; Float; Doom; Venom; Death; Poison; Heat; Mini; Silence; Confuse; Sleep; Freeze; Trouble; Berserk; Regen; Vanish;
Steal item: Ether, White Robe, Rebirth Ring
Battle Strategy:
For these next battles, it really helps if you are maxed out on Hi Potions. Get rid of all your normal Potions, if you haven't already. They will have no use. Whatever four characters you bring into this battle, you will have the upper hand on Kuja if you bring them in equipped with Auto-Life, Auto-Regen, Auto-Reflect, Auto-Potion, and High Tide. If you have to choose between them, leave out Auto-Reflect. It's nice, but not totally necessary.
As for characters, go with the ones that you feel best fit your style of play. However, a few general strategies for the use of characters are recommended. Zidane can serve a double purpose in this battle, attacking when needed (Thievery comes in useful here), and if necessary, using a turn to use an Elixir or Phoenix Down. If you bring Dagger, try to equip her with the Concentrate ability, as she will be able to probably bring the whole party up to full strength with one Cure 3. If you have Auto-Reflect, equip Vivi with Reflect x2 and cast Flare on one of your party members; if not, just have him Focus and cast it normally. If Steiner has the Ragnarok, he should use Shock every turn. Amarant's Aura and Spare Change abilities can be very useful. If you have Freya, using a maxed out Dragon Crest can deal an enormous amount of damage. Eiko should always be ready to cast a Full-Life or Phoenix in case someone does get killed, and Quina should be using the strongest Blue Magic that s/he has, and can also heal with White Wind if need be. Use Trance skills like Grand Lethal as they become available.
Anyway, just take your characters into battle fully prepared. Start hitting him with your best attacks, making sure to keep your party's HP at maximum as much as possible. Kuja has several attacks that he can use on your party, including Flare, Holy, and Flare Star, and can also cast Reflect on himself and heal with Cure 3. His attacks will become more frequent as the fight progresses, and near the end he will be attacking you after every move you make