Its in-game description reads "Dark armband with the power to destroy all." It's a quite powerful armband, and you can charge it, so you can fire stronger projectiles of magic. It is often found in the Moon Flower Palace. You can only find the Desctruction Brassard in dungeons' chests, but the build up is the easiest and probably the fastest way to obtain it. You cannot buy or invent this weapon. This armband is a medium-tier weapon (Tier 6) : it'll gain 4 Synthesis Points (SP) per level-up.