I've been grinding the achievements for this game with this one being one of the last ones I needed to get and saw that a few people were after a list of armour. Here are all the armour sets that I picked up and where I remember getting them (apologies if some are incorrect).

Starting Armour
Aztez

Early Game Festival
Chichimeca I
Commonor
Conscript (this one is named Conscript on the card but Common Warrior in the Loadout screen)
Eagle I
Jaguar I
Noble I
Porter (I recall picking this one up but it doesn't appear in the Loadout screen)
Priest I
Underworlder I

Mid-game Festival
Chichimeca II
Eagle II
High General
Jaguar II
Noble II
Priest II
Underworlder II

Carnage Festival (need the Playing Ball common/uncommon item to trigger)
Chichimeca III
Eagle III
Jaguar III
Noble III
Priest III
Shorn One
Underworlder III

Conquistador Item Drops
Conquistador I
Conquistador II
Conquistador III
Emperor (This one may be available in Carnage Festivals as well)

Also, I had the following weapon skins (just in case you need these too)
High Military Weapons (Mid-game Festival)
Mythical Weapons Set (Carnage Festival)
Spanish Weapon Set (Conquistador Item)