Final answer:
The prophecy regarding Achilles' birth foresaw a heroic but short life if he engaged in battle. Despite efforts by his mother Thetis to hide and protect him, Achilles was ultimately drawn to warfare, which led to his becoming a legendary Greek hero with a singular vulnerability - his heel.
Step-by-step explanation:
The prophecy surrounding Achilles' birth indicated that he would have a short but glorious life if he chose the path of warfare. To protect him, his mother Thetis hid Achilles away as a child and had him reared by the centaur Chiron. Later, to keep him from joining the Trojan War, she disguised him as a woman and hid him among a princess and her court. However, when Odysseus arrived with weapons as part of a ruse to recruit him, Achilles was unable to resist revealing himself by eagerly grabbing the weapons, thus fulfilling part of that tragic prophecy.
Achilles is also known for his invincibility which stems from being dipped in the river Styx by his mother. However, his heel, where she held him, was left vulnerable, which gave rise to the term 'Achilles' heel' as a metaphor for a person's weakness. Achilles' fate was to die as a great hero, as was depicted on the ancient Greek amphora featuring Achilles and Ajax by Exekias, highlighting the importance of fate in the stories of Greek heroes.