Jumbo Flan is immune to physical attacks and absorbs all elements. It has Reflect that cannot be dispelled, but it is susceptible to Slow if the player bounces the spell off a party member (the member must have Reflect status).
The battle should be started by casting Reflect on one party member and bouncing Slow off of them to slow down the Flan. Then Anima should be summoned and buffed with Haste and Shell, optionally five boosts of Focus, for both fortified effects of cure spells and reduction of Jumbo Flan's offensive spells. After that Anima should use Pain 2-3 times, depending on her agility, each turn. If Jumbo Flan uses Regen it should be dispelled right away.
If using a regular party, the battle should still be started by slowing down Jumbo Flan. Then the party should get ready by casting Haste, Shell and Focus on everyone (and dispelling any characters of Reflect). The party should then proceed by Doublecasting Flare or Ultima. Holy also works but cannot be doublecasted.
The characters that should be used are Yuna and Lulu as they boast the highest magic power. Lulu's fully powered Celestial Weapon also offers Magic Booster and One MP Cost effects which are perfect for this battle, and if one received Dark Matters from catching monsters for Arena, another weapon can be created with Break Damage Limit, One MP Cost, and Magic Booster.
Overdrives are effective because they are neither physical or magical, but due to Jumbo Flan's defensive stats, their damage is significantly reduced when compared to spells or Anima's Pain attack.