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Astral Attire
Collect any armor set from The War Within PvP Season 3.
Astral Attire requires collecting any complete armor set from The War Within PvP Season 3, which can be done by purchasing the full Astral Aspirant's set with honor from Velerd in Dornogal.
Earn 6475 Honor
You need 
6475 honor total to purchase a full set. The Comp Stomp Brawl is a good source of honor if you need to farm it quickly.
Visit Velerd in Dornogal
Go to Velerd at 55, 76 in Dornogal's PvP area and purchase the full Astral Aspirant's armor set for your armor class — for example, Leather Helm, Leather Spaulders, 
Astral Aspirant's Cape, Leather Vest, Leather Wristwraps, Leather Gloves, Leather Belt, Leather Breeches, and Leather Boots. You can find the set listed under Dunewalker → Aspirant in his shop.
Equip Every Piece
Equip each piece of the purchased set — the achievement only triggers once every item is worn, which also makes the pieces non-refundable. If the achievement does not pop immediately, try logging out and back in.
Tips
Purchasing any piece of honor armor adds a chat message you can click to view the full set, which helps confirm you have every slot covered before spending all your honor.