Keep in mind, the classical heroes were understood, more than anything else, in term of their exploits. They stood at the pinnacle of human achievement, with feats that others would not have dared to attempt. With this in mind, Theseus would certainly qualify as a hero, given his various adventures, as well as his status as the definitive hero of Athens.
As a child, Theseus was set with a task to prove himself: his father, Aegeus, king of Athens (interestingly, Theseus had two fathers, the mortal Aegeus, and the god, Poseidon) had left a sword and sandals buried beneath a rock. When he'd grown to adulthood, he was to retrieve the sword and sandals, and then travel to Athens to present himself. So begins one of his most famous series of adventures.
During this time period, the road to Athens was plagued with dangers. Theseus confronts these dangers one by one, completing a total of six labors: slaying Periphetes, Sinis, the Crommyonian sow, Sciron, Cercyon, and Procrustes. Throughout these encounters, he has a tendency to turn the tables on his would be murderers, killing them in the same fashion that they had killed so many others. Later, after having cleared the road of these dangers, he would arrive in Athens, with further adventures still ahead of him.
There are numerous stories about Theseus. He's very much a larger-than-life kind of character, and that very same larger-than-life quality is what defines what it means to be a hero in the Classical World.