This is a difficult question to answer, because when it comes to ancient mythology, there are different of sources and many sources that we have lost; in other words, these sources are no longer extant. In light of these points, we can say a few things.
First, according to our most ancient sources, Achilles was born from the union between Thetis (a nymph) and Peleus a human. This human/divine union is important to consider, because this makes Achilles a demi-god. For this reason, we can say that in part Achilles became powerful due to his one divine parent.
Second, according to the poet Statius from the 1st century AD, Achilles' mother, Thetis, wanted to make Achilles immortal by dipping him into the river Styx. Because Thetis held Achilles by the heels, the only place where Achilles was vulnerable was his heels. We can read about this in the work, Achillleid.
The problem with Statius' tale is that it is not found earlier. This could be because he made it up or because we lost earlier sources.