According to prophecy in Greek mythology, Achilles was destined to die young, either by his own choice to fight in the Trojan War or to live a long, uneventful life. His mother, Thetis, attempted to prevent this fate by dipping him in the River Styx to make him invulnerable, but his heel remained a weak spot, leading to his eventual downfall. This prophecy highlights the themes of heroism and fate that are prevalent in Greek myths, emphasizing that even the mightiest could be doomed by their own choices.