The achievement unlocks when you pick up your tenth unique weapon. Unique items are denoted by purple
nomenclature. They can be weapons, armor, or accessories. Only weapons that can be equipped in the primary or secondary weapon slots count towards the achievement.
As the description states, weapons acquired from the special delivery chest in Gorhart are not applicable
. Once a unique weapon is picked up, it counts towards the achievement even if you do not keep it in your inventory. You may sell unique weapons, discard them, and/or place them in a stash chest without voiding the achievement.
Pick up unique weapons up as you come across them. They may be in chests, piles, enemy drops, and so on. Old lootable skeletons are a good source of unique weapons. You can also pickpocket enemies and NPCs for unique weapon or steal property. The 20 second video below depicts acquiring the tenth unique weapon and popping the achievement: