Achilles's father was Peleus, king of Phthia in Thessaly, and his mother was Thetis, daughter of Oceanus. When Achilles was a baby, his mother held him by his heel and dipped him into the river Styx. This would make him invulnerable to any weapon. But by holding onto his heel, that part of his body was vulnerable. That was the cause of his downfall in the Trojan War.
Achilles's mother had warned him that he was destined to spend either a long and comfortable life at home in Phthia or a short, glorious one in the Trojan War. Achilles chose glory instead. She also warned him that he must not kill Tenes, king of the island of Tenedos. Tenes's father was Apollo, the sun god, who would surely take revenge for his son. Of course, Achilles fought against the Trojans in the war and killed Tenes.
Achilles was killed by Paris, who shot him with an
arrow from behind the Trojan walls. Paris's hand was guided by
Apollo who took revenge for the death of his son. The modern phrase,
their 'Achilles heel,' for a person's weak spot was derived from
this myth.