Achilles was a Greek warrior who fought in the Trojan War. He and Hector, son of King Priam of Troy, were fighting when the First Doctor arrived in his TARDIS. The arrival of the Doctor distracted Hector, allowing Achilles to slay him.
Achilles saw the Doctor emerge from the TARDIS and, marvelling at this power, came to believe that he was the Greek god Zeus, who had taken human form and descended to Earth. He brought the Doctor to Agamemnon, Menelaus and Odysseus, the King of Ithaca, who was considerably more sceptical.
Priam intended for his son Paris to kill Achilles, but instead Achilles was killed by Troilus, Paris' younger brother. (TV: The Myth Makers)