How do you get the gaia armour?

You need to get the "Earth Armour" design, which you can get from Selepation Cave. The you can then make the "Gaia Plate" for Clavats which has 30 defence points. You also need the materials Lords Rode x1, Orichalcum x2 and King's Scale x1. I don't know what cycle, although I would guess at the 3rd one.

Design: Earth Armor (Clavat)
Armor: Gaia Plate
Materials: Lord's Robe, King's Scale, Orichalcum x2, 5000 gil
Defense: 30
This is the ultimate armor of Final Fantasy: Crystal Chronicles. From the
Manual, you will find that Clavats are specializing in defense, and the
Presence of this unique armor is there to prove it. With 2 chunks of the
Rare Orichalcum, the Lord's Robe of the Gigas Lord of the Moschet Manor,
The King's Scale of the Lizardman King of the Daemon Court, you get the
Finest materials from all over the world to produce the Gaia Plate. Finding
The design for this armor is another story. To find it, you must beat a
Boss with a high score and hope that it will be up for grabs in the Item
Selection Screen. Then, you will have to beat the Gigas Lord and Lizard
Man King with high scores and hope that you get to salvage them in the
Selection screen. All this effort will pay back in the air. Just don't
Lose heart, all you Clavat players out there!