Some points of information

Rating: 8/10 (17 May 2004)

In Greek myth Briseus was Achilles' favorite slave girl. Chryseis, a priestess of Apollo, was a prize of war for Agamemnon. Achilles forced Agamemnon to return Chryseis to her father, a priest, to appease Apollo, who had caused a pestilence to descend on the Greek troops as punishment for her capture. In retaliation, Agamemnon deprived Achilles of Briseus. In the movie, the two characters are nicely combined in a way which strengthens Achilles' connection to Priam.
The story of the killing of Achilles by Paris shooting Achilles through the heel with an arrow is not found in Homer, but in a later poem called Aethiopis by Arctinus.
According to legend Achilles' mother was a sea nymph named Thetis. In the movie, Julie Christie definitely plays a mortal, not a goddess, although one of the characters mentions his lineage from the gods. According to Homer he was raised by his mother with his inseparable companion and cousin Patroclus. One of the non-Homeric tales of his childhood tells of Thetis dipping him in the River Styx by which he became invulnerable, except for the part of the heel by which she held him.
The character of Aeneas is in the Iliad and he survives the Trojan war, but the handing off of the Trojan sword for the future founding of Rome is pure Virgil.
I hope you get to see the movie. It's not perfect, but there's lots to recommend it.