Sorry, not many people have been using this Wiki lately and I haven't been updating the site or following the Discussions at all.

For each of the events that use them, the "First" through "Tenth" armors are only for use in the "Boss Collection" menu (menu, Boss Collection, "Special" collection); the armors are not intended to be used/equipped at all otherwise. You can fuse them away (use them to enhance other armors) as soon as you redeem your rewards.