Like Heracles, Perseus is assigned to complete a seemingly impossible task (though he only has one task instead of twelve). In the story of Perseus and Medusa, King Polydectes sends Perseus on a quest to retrieve the head of the ugly, terrifying gorgon Medusa. Perseus brags that he can bring King Polydectes anything, and so he agrees to complete this "impossible" task. (Really, King Polydectes really just wants to get Perseus out of the picture so that he can marry his mother, Danae.)
With the help of Hermes and Athena, Perseus locates the Graeae, three nasty old hag sisters who share one eye and one tooth between them. Perseus is able to convince them to tell him where he can find the Nymphai, three nymphs who have some of the gods' treasures in their safekeeping.
Perseus finds the Nymphai and convinces them to lend him Hermes' winged sandals, which allow him to fly, Hades' helm of darkness, which makes him invisible, and the kibisis, a bag so tough it can hold the toxic head of a gorgon. Perseus travels to the seaside cave of the gorgons where he successfully severs Medusa's head (and manages to not be turned into stone in the process).
Perseus returns home and turns King Polydectes and all of his men to stone, saving his mother.
Read all about Perseus' quest to get Medusa's head here.