The Dual Blades are a great choice, as they let you cover plenty of ground while dealing out damage with the B/Circle attack. Alternatively, the Bow or Light Bowgun is a good choice for fighting the Kirin, as it allows you to attack from range while also continually being on the move.

Fast-hitting weapons like the Sword and Shield and Dual Blades are great for applying status effects. Their mobility also makes it easier to catch up to the Kirin as it hops and trots around. Hammers are also exceptionally strong against Kirins outside of the sleep strategy.