Achilles was the son of Peleus, king of the Myrmidons, and the nymph Thetis, thus he was a mortal/divine hybrid. At his birth, his mother tried to make him immortal by dipping him in the River Styx in Hades, but he remained vulnerable at his heel, where she held him while he was immersed.
Our term “Achilles heel” comes from this incident, and refers to a weakness or vulnerability, leading to undoing, particularly in someone or something with an otherwise unusually strong constitution.
Achilles was the greatest warrior of his age, the Greek hero of the Trojan War, as recounted in Homer’s “Iliad”, but he was not without character flaws. His rages were legendary, his pride at times insufferable, and he was quick to take offense, as when Agamemnon, leader of the Greeks, claimed as prize a Trojan maiden whom Achilles fancied. He refused to fight after this insult, and remained sulking in his tent until the death of his boon companion Patroclus, at the hands of the Trojan prince Hector. Achilles famously killed Hector, afterward dragging his corpse, tied to his chariot, around the walls of Troy. He was himself killed by Hector’s brother Paris, who shot him in his one vulnerable spot with an arrow guided by Apollo.
Astrologically, Achilles’ primary usage is as a point of weakness or vulnerability, but it can also denote strength, a military connection, uncontrolled anger, vindictive vengeance, mulish obstinacy, sulkiness and staunch friendship.