Hayou no Tsurugi: Shikkoku no Mashou

Rasutel, a resident of the Floating Castle, is tasked with retrieving a kidnapped princess, having been chosen by the Demon-Breaker sword. This sword is a powerful artifact wielded by the castle's inhabitants to battle demon beings. Her quest is complicated by her younger brother's desire for her golden eyes, a family heirloom that could give him the power of their father, the Golden Youshu. She is also aided by Anshu, a unique Youki who assists her on her mission.