As far as I can tell, there are a few ways to "Loot" a weapon. Throughout the world in the game, you'll see weapons on the ground you can pick up and use, but picking one of those up will not pop this achievement. You actually need a weapon you can equip through the menu, and then summon with varying amount of filled shards, depending on the weapon.
You can get a weapon by joining a school and leveling it to level 6 through pvp combat, which will then let you equip and use the school's weapon as long as you are still in that school. When you kill either of the first two bosses, you will also get a weapon that you can equip and use whenever you want. You can also buy one from the essence store at altars by spending the fragments can sometime get from defeating enemies.