Drakan: Order of the Flame

The game follows Rynn, a young woman with extraordinary martial skills, and an ancient dragon Arokh on their quest to free Rynn's younger brother from the evil sorcerer Navaros. The gameplay alternates between dungeon exploration and monster fighting when Rynn is alone and aerial dogfights when she mounts Arokh. Source: Wikipedia, "Drakan: Order of the Flame," available under the CC-BY-SA License.