Here is Thomas Banks’ 1789 sculpture of Thetis dipping baby Achilles in the river Styx. (Photo by me back in Feb. 2020 at the Troy exhibit.)
The myth of Achilles’ invulnerability seems to be a later addition to the myth, but we can’t be sure given how many ancient texts have been lost. Homer does not allude to Achilles’ invulnerability nor, to my knowledge, are there references to it in literature of the classical period. In Jason and the Golden Fleece, Apollonius includes a story of Thetis attempting to burn away Achilles’ immortality and being interrupted by Peleus before she can complete the ritual. But neither Styx nor heel is involved.
The earliest reference to the heel story seems to be in the Achilleid by Roman poet Statius, but the casual way he references Achilles’ dip in the Styx suggests Statius himself did not invent the story. So many unsolved mysteries from antiquity!
What’s an ancient mystery—mythic or historical—that you wish could be solved?