Perseus didn't kill Andromeda. He saved Andromeda from the sea monster summoned by Neptune/Poseidon. I think that you are meaning Medusa
Hermes gives Perseus guidance and a sword stronger than the Medusa's scales. He tells Perseus that to fight the Medusa Perseus will need special equipment from the Nymphs of the North. Their location is a mystery, and Perseus must ask the Gray Women, three sisters who live in a gray land and are gray themselves. They share only one eye among the three, and they alternate using it. Before Perseus sets out to find them, Athena gives him her shield and tells him that he must look at the Medusa through the shield, like a mirror, in order to avoid turning to stone