Defeat Tier 2 VNM Capricornus 6 times. He can be found in Jugner Forest, Jugner Forest (S), East Ronfaure and East Ronfaure (S). See page for Voidwalker Notorious Monsters for more info on spawn conditions.
Trade your Mozu (Attack +7) to the Magian Moogle in Ru'Lude Gardens to accept this quest.
He will give you back your, Mozu now inscripted with Trial 585.Once you are finished killing the Mobs, trade the Mozu (Attack +7) back to the Magian Moogle and you will recieve your new katana, Mozu (DMG +7).
Everyone in party with quest started and have Mozu (Attack +7) equipped will receive credit for the kill as long as you are within xp range.