The achievement of arete (courage) was very important for the Greek citizen, especially a warrior. Do Hector and Achilles achieve arete in the Iliad?
I believe Hector does, in fact, achieve arete. I have a more difficult time believing that Achilles does.
Hector was everything a Greek hero should be. He was loyal to his family and country, brave in the face of insurmountable odds, truly a self-sacrificing individual. He most definitely achieved arete before being killed in battle.
Achilles, however, spends most of the Iliad sitting out of the battles, sulking because of Agamemnon's insult to his pride over the slavegirl, Briseis. Rather than sucking it up and leading his men as he should have done, he stayed behind, raging over the loss of his honor--causing far more loss to his honor by his own inaction than what was caused by Agamemnon's insult. Although Achilles could have fought, he chose not to. In my opinion, that means he did not achieve arete.
Check the link below for more information. Good luck!
In my own reading of Arete, it means, not just courage, but translated as "virtue". It means some inborn talent or capacity a person has that they have developed into excellence. So Achilles has Arete, "a fighting fiery spirit."
This spirit is related to his equally fiery temper. Unfortunately his fiery temper the downside fo this Arete gets him into problems, and probably partially explains how he treats Hector dragging him through the mud dragged by his chariot. Check out website: http://faculty.gvsu.edu/websterm/Read_Iliad.htm
This is where I got this information from which has really expanded my idea of Arete.