Thetis knew that Achilles was going to be in a duel. She ran for a long time to Hephaestus, her friend, who makes wepons armor. Finally, when she gets there, she goes to Hephaestus out of breath and asks him, " Please stop what you're doing, and make a suit of armor for Achilles, my son."
When Achilles tried the armor on, it fit perfectly. Achilles was fighting Hector because, Hector killed Achilles' friend thinking it was Achilles. The God was more than mad and sad, he was raged and depressed and Hector refused to let anyone help him fight Achilles was ready for battle. When Hector and Achilles were ready, Achilles gave a speech and then said "CHARGE!"
Once the battle started, Hector was thinking and second-guessing himself. If he ran into the Trajan gates and backed away, he would be called a coward for the rest of his life. Achilles started charging at Hector, but Hector was to fast and started to run. They were both out of breath when Athena told Achilles, "Catch you breath, Achilles". She also told Hector it was now time to actually fight.
Hector then knew it was time and he needed to face his fate so he told Achilles, "Achilles, I won't run anymore. I'll fight and kill or be killed..... If Zeus allows me to kill you, I promise no outrage will happen to your body. All I will do is strip you of your armor, and I will give your corpse to your men untouched. Will you do the same for me?"
Achilles disagreed and threw his spear at Hector, and missed. Hector started mocking Achilles and threw his spear at him and it hit Achilles' shield. Then, with Achilles' second spear he hit Hector in the chin. Achilles looked down at Hector who was now pinned to the ground by the spear, "You killed my friend Patroclus, and so you will pay for that. The dogs and carrion birds are going to chew at your guts while Patroclus burns on his pyre with due reverence to the gods."
Hector begged Achilles to have mercy and give his body to his family, but Achilles refused. But Hector reminded him that the Gods would not forgive him if he killed Hector. But yet again, Achilles opinion didn't change. And at that moment Hector died. Achilles got his horse and chariot, and tied Hector on to the end and rode around the battlefeild dragging him around.