Defender X
HP - 64,000
AP - 6,600
Weakness - None
Steal - Lunar Curtain
This guy has no weakness, but you can make him have one. Cast hastega on the party. Then have Auron use Armor and Mental break on Defender X to make him much weaker. Use Waterga on Defender X to make his HP deplete quickly. Use Dark attack on Defender X also to keep him from attacking you also. This battle is hard and then easy. Use Cura or Curaga alot, you'll need high HP. Don't forget your aeons!
After the battle is over, be prepared to get a secret aeon, Yojimbo. Before you go get him, make sure you have over 200,000 gil to spare. Go down the hill or whatever and go into the Cavern of the Stolen Fayth. Follow the red area, until you battle Yojimbo. Who is owned by Lulu's first summoner to graud. But she's dead. And you fight her...? Oh well. After you defeat him, which is easy, head to the red arrow on the map. Then he'll make a bargain with you for 200,000 Gil for his services as an aeon. Any time you triple that amount, he'll give you 2 teleport spheres for the sphere grid. Yippie! Then head back out to where you fought Defender X and head across the bridge following the red arrow.