When you defeat each golem prototype, you receive the matching crystal. Defeat the Azure Gladiator, you get the “Azure Crystal”, #200 in the item list, with the description “Enables the Azure Gladiator improved prototype to be summoned when necessary.” If you click on “Items” to use an item, the crystals do not appear in the list, either at rest or during a battle. Perhaps only available in a special battle? Or is it just a trophy? The same situation applies to the other three crystals.
Kulanda, in Reyarnea Village, tells you to “make use of it if you need to,” but make sure to repair any damage to the golems. So there must be battles ahead, but where? If you have a ship, go to that tiny snow covered island in the northeast of the outer world and enter the cave. If you don’t have a ship….see the post about that.