It's time to make your guys über badass. Hold start and press circle. A map will come up, this will let you see the world. Look at the yellow dot at the middle-top of the world. That's the Citadel of Trials. Parking won't be easy, you'll have to find a spot very far away to get to it.
When you enter the Citadel of Trials. You'll have to walk through a bunch of pillars. Talk to the silly sage and he'll tell you about how hard this place is. Smack some sense into the old bastard and he'll leave. Go to the top left and enter the door. Walk into the chair… and your challenge begins…
You'll be teleported to a little room. Leave the room and walk onto the pillar. You'll be transported to another little room, walk up into this pillar too. In the next room there will be two pillars. Take the bottom one. Next room: There is only one pillar in this room, take it. Take the bottom one here. Go down the long hallway and take the one at the bottom. Now take the one that's closest to you. Go straight over, get the treasure. You'll have to fight two clay golems. Take the gauntlets, and leave the room. Take two steps to the left, and go straight down into that pillar. You'll come to a room with a staircase, take it up.
Now, this is pretty self-explanatory. Go straight up till you enter a door. In here you'll have to fight some nightmares for the treasure chest at hand. Run across and get those treasure chests too (Ice brand, Steel Glove, Ruby Armlet). Then run down and get more chests (Cottage, 1455 Gil, 7340 Gil). Finally, run over to the right and get the "Rat's Tail". Right when you're about to leave you have a fight… After the fight make your way back to the airship. Go directly south of the Citadel of Trials to…