Perseus and Andromeda
Susanoo and Yamata no Orochi
Japanese mythology has its own Perseus-like hero named Susanoo. In the myth of Susanoo and Yamato no Orochi, Susanoo, Susanoo happens upon an old couple and their beautiful daughter. They're all crying because the girl, Kushinada, is about to be eaten by a giant serpent named Yamato no Orochi. The hero says that he'll fight the serpent if he can marry the beautiful Kushinada. (This sounds a lot like Perseus' story, doesn't it?) The girl's parents agree, and with a good sword and a bit of trickiness, Susanoo kills the monster and saves the girl.
The story is pretty fun, so be sure to read the whole thing here.