People who deeply love themselves are able to make mistakes and receive constructive feedback without spinning into self-condemnation. I believe that the core of this complex is shame; a belief and feeling that we are not good enough, bad, gross, not enough, inferior, rejected, unlovable, etc.
So, the direct anti-dote is to cultivate loving-kindness. Not just as a concept but as a felt experience. Loving-kindness meditation is a direct anti-dote to shame and it's resultant perfectionism.
Hypnotherapy can really help someone quickly shift out of the shaming/perfectionism trance. And then self-loving kindness meditation is the long-term cure.