Did Hector have a realistic chance of defeating Achilles?

No. He did not. Both Eleftherios V. Tserkezis and Tyler Smith wrote excellent answers. I'll do my best not to repeat their points. In the scope of the epic, Hector was always doomed to die. read more

In killing Hector, Achilles satisfied a grudge. For the Greeks, it meant the war was essentially won. No one could replace Hector. His death was Troy’s defeat. However, Achilles never fought to win the war for the Greeks. It was a personal matter for him, getting even with Hector for taking the one person who mattered to him: Patroclus. read more

Achilles says there are no binding oaths between lions and men. He adds that Athena will kill Hector in just a moment. Achilles hurls his spear, but Hector ducks and it flies past. Hector does not see Athena retrieve the spear and return it to Achilles. Hector taunts Achilles that he didn't know the future after all. Then Hector says it's his turn. read more