Hayou no Tsurugi

Laethreel, a young demon hunter, receives the mission of rescuing the princess of Gandia from the cluthces of a wicked noble demon named Aju. On her journey she is accompanied by her unpredictable and blood-thristy sword, Grenki, and a sweet-talking demon named Anshu, who claims to be her ally. Little does Laethreel know that on her mission, she won't face only beasts but also the dark conflict of her origin.

(Source: Anime News Network)