In the southeast of the world map, there is a small island where a cactus pops up from the ground. Land and fight. These little flighty cacti give 20 AP apiece, however, are prone to run off before defeat. Be quick and raise your accuracy. LEARN THOSE GF ABILITIES! Approach the little pop up cactus on the map to fight Jumbo Cactuar. Be not fooled, he is TOUGH. Especially that 100,000 Needles attack, ouch. Be sure all your characters can revive a lost character. He has a LOT of hit points. He is weak against water, so junction 100 waters to your attack. Use Aura, water, Shiva and Leviathan GFs if need be. Draw MELTDOWN and cast it on him. Besides the Jumbo Cactuar, the only other place Meltdown is available is from monsters called Gayles in the snow field area(Thanks to John Yip for that factoid).
Make sure you stock as many of this spell as you can. Hope Squall uses the Lionheart on Limit breaks, use Irvine’s AP ammo, or the best you have. Though not a powerful GF, he is the only one who allows Luck and Evasion junctions. He only deals as much damage as the first digit of his level multiplied by 1000. Therefore a level 67 Cactuar would deal 6000 damage.