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In Greek mythology, there are characteristics usually followed in order to identify someone as a hero. These archetypes are the following:

1. He should have a mother who's both of Royal blood and a virgin
2. His father should be a king.
3. Fathers are usually related to mothers by blood
4. Heroes are conceived unusually
5. The hero is the son of a god
6. There is an attempt to kill the hero in infancy, often motivated by greed, envy or prophecy. The usual killers are paternally linked (father, grandfather)
7. The Hero flees from danger
8. And is often fostered in a distant land.
9. There are no accounts of growing up as a child
10. Is set to return to his home after a victorious quest
11. Marries a beautiful maiden (often princesses)
12. He becomes the king

Perseus possesses these archetypes, and is often noted with his heroic quest of killing Medusa. 

Now this, is, in Greek mythology, heroic. He got rid of a dangerous creature that can wreak havoc to the people any time she wants, but I think the most heroic deed Perseus performed happened after the killing of Medusa.

He freed Andromeda, and got rid of Atlas' struggles. These deeds, albeit done after the main quest, are what makes Perseus heroic. 
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