Have the person you want to gain Sphere Levels have a Triple AP weapon, gained from killing the Arena Monster One-Eye. Eventually it'll drop them, try to get one for the character you want to level up, and try to have it have at least two other slots.
Put Triple Overdrive and AP->Overdrive on that weapon.
Now for the other two characters (most likely a physical attacker like Auron, Wakka, or Tidus), give them both armour with Auto-Phoenix and Auto-Haste. Maybe do the same with the leveling up character. Or hey, do all of this for all three, but you only need to level up one character at a time.
Now, set everyone's Overdrive mode to "Ally". Make sure to have 99 Phoenix Downs.
Go fight Don Tonberry in the Monster Arena in the Calm Lands. You should be able to do enough damage for at least 7,000 damage, that way you can actually kill it eventually. Have the two people you're not leveling up attack him, so Don Tonberry counter-attacks and kills them. They then should be revived with Auto-Phoenix. And thanks to Auto-Haste, you lose no turns!
Now, for how the trick works, you'll see that your people keep dying. That's a good thing, for this. Thanks to Overdrive->AP, you gain AP when your Overdrive gauge fills. Thanks to 'Comrade', it fills when your allies take damage. Thanks to Triple Overdrive and Triple AP, that's 9 x AP whenever the Don shanks one of your allies!
Eventually Don Tonberry will move in closer and just use Knife for 9,999 damage. Fear not, he can still only kill one person at a time, and if two of your people have Auto-Phoenix, you can't die. Keep attacking him until he dies, if you're doing a constant pattern of attacking anyway. After the battle, you should get a little over half a million AP.
I made Yuna a walking god, how 'bout you?
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*Yeah, this trick makes leveling up a joke, but if you aren't a person with morals, it may not matter to you anyway.
Any other questions, I'll be glad to answer.