He was slain by Paris during the final days of the siege to Troy, by means of a poisoned arrow shot in his heel.
And I think the mother didn't dip him twice because once meant invulnerability, twice meant death. No mortal could have withstood the power of the waters of the Styx twice. I simply wonder why she didn't hold him with a rope or at worst by a finger which she could then have cut. I guess the myth wouldn't have been that interesting, just like playing a FPS in god mode
