What is required for a mother to file abandonment charges on a father?in order to get his parental rights revoked?

You don't file abandonment charges. What you do is file a petition to have parental rights terminated. You can CLAIM abandonment as grounds for the TPR, but you better have something else going for.

Generally courts will not grant a TPR, especially involuntarily, unless there is someone waiting to adopt the child or the parent represents a danger to the child.

If he has abandoned the child, then why do you need do anything anyway? He's effectively, if not legally, relinquished his rights.