Lost Universe

Kane Blueriver, a trouble contractor, is being hunted by a criminal syndicate named Nightmare because he pilots the Lost Ship Swordbreaker, the only hinderance to Nightmare's plan to spread the dark lord Dark Star throughout the galaxy. Kane, along with Millie, a girl who dreams to be the "best in the universe," and Canal, Swordbreaker's AI, vows to defeat Nightmare, who, besides having a sinister plan, killed Kane's grandmother many years ago.

Synopsis from Anime News Network