Probably the closest story to the tale of Perseus and Andromeda is the story of St. George defeating a dragon, which was really popular in medieval Europe. The story goes that St. George, a noble Christian knight who is traveling in Africa, comes upon a beautiful princess tied up beside a lake. It turns that the lake is the home of an evil dragon, who will destroy the land unless the princess is fed to it. Brave St. George tells her not to worry and slays the evil dragon with ease, converting all the Africans to Christianity in the process.
Interested in the heroic St. George? You can read the story of his run-in with the dragon here.