This is based on how I beat Ultima Weapon (UW).
Party: Zell, Squall, Rinoa
Levels: Zell-high 70's to 80's HP: 7052 Squall-100 HP: 9999 Rinoa (a little higher than Zell) HP: 9999
Weapons: Zell-any Squall-Lion Heart Rinoa-any
Junctions: Zell-high HP, highspeed, magic Squall-high strength and HP Rinoa-recover (revive optional), high vit. , magic, initiative, high speed
Magic: Zell-aura, meltdown Squall-whatever (max out HP) Rinoa-Life, meltdown

Note: use move-find to use the save point by the pilliar RIGHT before you activate the Ultima Weapon sequence.

Ultima Weapon's attacks

:
Light Pillar-fatal. 9999 damage to one party member
Quake- Earth-elemental damage (1,000-2,000) to all party members. Can be avoided with float. Equip life or full-life to elemental-defense to lessen attacks.
Meteor- attacks all party members. (0-1,500/2,000) per member. Shell lessens attacks.
Sword (unsure of actual name)-2,000+ damage to any one player (usually one that has just been revived). Can be lessened with shell (?).

How to Beat Ultima Weapon

~Have Rinoa draw Eden from Ultima Weapon
*may use Light Pillar* either Life Rinoa, or leave Zell.
~Rinoa uses meltdown (or Zell, if he's not down)
~(Zell uses aura on Squall)
~keep Rinoa around 9999, let Squall use limit breaks, let him get killed, use life, let use limit breaks, and so on.
~keep using Recover on Rinoa, NEVER on Squall (we want to keep him 2,500 (if at 9999) or in the yellow, so he can use his limit breaks).
~hope he uses Lion Heart (can only be used if Lion Heart is Squall's weapon)
~Lion Heart takes Ultima Weapon down in one beating, just make sure you have Eden before attempting Lion Heart.
Note: Does increasing Squall's Luck stat better his chances of him using Lion Heart?

Congrats! You've beat Ultima Weapon, and you have Eden, considered by many the most powerful GF in FFVIII! Use Move-Find again to use the save point, and get the heck outta that place! (there are less monsters on your way back up).

I beat this "thing" in less than a day with this strategy. Hope it helps you! (I already knew the damaging power of Lion Heart before the battle).

~End of lesson~