Looking not just at achilles, but also at hector, how do they both appear to represent ideals of heroic action?

Both Achilles and Hector represent ideals of heroic action, such as strenght, bravery, loyalty, manliness and agility, but they're different from each other.

Achilles was the son of an Olympian goddess, so he was a demigod, this meant that he was brave, handsome and loyal because that was in his blood. Nevertheless, Achilles had some flaws that also made him the hero - and the part human - he was. He had a vulnerable heel and at times he had ungovernable rage, and this led him to kill and torture Hector.

Achilles was not married and he did not have children, he only had his mother, Thetis.

On the other side of the story, there's Hector. He was human, he didn't have any divine blood in his veins, and he was a father and a husband. Also, Hector was a Trojan Prince and because of his humanity, he was humble, unlike Achilles who was arrogant. Hector didn't have a god father or a goddess mother, so he had to learn his bravery, strenght, loyalty and agility by himself because he was not a demigod, he was just human.

Both men represented the ideals that heroes represented, but they were also different and those differences made them who they were, loyal and strong men who fought for what they believed.