Defeat 400 bird-type creatures where you gain exp.
Trade your Koruri (Attack +5) to the Magian Moogle in Ru'Lude Gardens to accept this quest.
He will give you back your, Koruri (Attack +5) now inscripted with Trial 586.Once you are finished killing the Mobs, trade the Koruri (Attack +5) back to the Magian Moogle and you will recieve your new katana, Isatu.
Everyone in party with quest started and have Koruri (Attack +5) equipped will receive credit for the kill as long as you are within xp range.
Good Location: When wind weather is rare in Wajaom Woodlands you can always find a party in Abyssea - Misareaux killing the Colibri there. It's not uncommon to find 5-8 there to team up with and get well over 100 kills in a single game day.
Note: Just for info, even if you will mainly be alone during all the 3.950 killing to reach the OaT 2-3 stage of Katana level 85, Sword and Great-axe share ALL the same monsters to slay.