To put it in the simplest terms, they were simply two warriors in opposing armies who met up and did what came naturally to them as warriors: they fought. However, Achilles had a grudge against Hector, since the latter killed the former's cousin, Patroclus.
The fight was short, and after Achilles defeated Hector by breaking his neck, proceeded to drag his corpse around the battlefield before letting the Trojans reclaim his body.
Interestingly, Achilles was killed a short time later by Paris (Hector's brother), who shot him in the ankle with an arrow (thus giving the Achilles tendon its name).
Hector, before their fight, promises Achilles that he would give him, if slain, a honorable burial.
Losing a fight with Achilles.
Athena pretended to be Deiphobos, one of Hector's brothers. She made a speech in the form of Deiphobos about the need for Hector to stand against Achilles. Hector believed her and decided to fight Achilles.
Hector was chased around Troy three times until Athena tricked him to stop and fight Achilles. Hector charged and missed, and Achilles slayed him. Hector had taken Achilles' armor and that was why Achilles chased him
In The Iliad, Book 22, Hector tells Achilles that should he (Hector) be victorious in their battle he will return Achilles' body to Greece and asks that should he die at Achilles' hand, Achilles should return Hector's body to Troy. Achilles refuses.
Achilles .
Yes, he did.
Hector, before their fight, promises Achilles that he would give him, if slain, a honorable burial.
Losing a fight with Achilles.
Athena pretended to be Deiphobos, one of Hector's brothers. She made a speech in the form of Deiphobos about the need for Hector to stand against Achilles. Hector believed her and decided to fight Achilles.
Hector was chased around Troy three times until Athena tricked him to stop and fight Achilles. Hector charged and missed, and Achilles slayed him. Hector had taken Achilles' armor and that was why Achilles chased him
In The Iliad, Book 22, Hector tells Achilles that should he (Hector) be victorious in their battle he will return Achilles' body to Greece and asks that should he die at Achilles' hand, Achilles should return Hector's body to Troy. Achilles refuses.
So the story says.
Achilles had already killed a number of Priam's and Hecuba's sons. They feared Hector might be killed as well.
Patroclus used Achilles armor to fight Hector when Achilles refused to continue fighting for Agamemnon. Patroclus was Achilles close friend and lover in the Iliad.
It is believed that Hector died in a duel with Achilles, in the tenth year of the Trojan War. Achilles first stabbed Hector in the shoulder. Hector fell to his knees and Achilles went for his final stab in Hector's stomach. (This was all after a long fight between them that went for some time). After Hector had died, Achilles tied Hector's feet to Achilles' carriage and ridded off with Hector's dead body dragging behind him.
Hector was killed by Achilles for retribution of Achilles cousin's, Patroclus's, death by Hector's hands. Hector was unaware that he had killed Patroclus as Patroclus had taken Achilles' place under false pretenses when Achilles refused to fight. While Hector felt guilty about killing the wrong person he fought Achilles anyway, knowing that he would not survive the battle.