Summarize the battle between Achilles and Hector. Make sure to mention how Achilles was killed.

Achilles' most notable feat during the Trojan War was the slaying of the Trojan hero Hector outside the gates of Troy. Although the death of Achilles is not presented in the Iliad, other sources concur that he was killed near the end of the Trojan War by Paris, who shot him in the heel with an arrow.