A second version of the same myth?

For the longest time, the version of Achille's immortality was one of the female gods disguising herself as an old maid, and becoming a nanny for the boy to become the great achilles. She held him over the fire every night, and when she was about to complete the immortal...ness, his mother came in, 'saved' him, scorned the old woman, who turned back into her godly self and spoke the truth of the matter, then left. Is this some silly variation? When I was a child I read so many books on Greek Mythology, and now I'm confused, because everyone I know knows the River Styx version...which is totally new to me. Can someone tell me what I read, and...just, what the hell? ><