Batman is the world's greatest detective. His villains need to compete on an intellectual level, and in fiction a doctorate is short-hand for "smart" and "an expert in the field."
My favorite moment from the old Batman animated show was when the rogues were sitting around telling their stories about how they almost got Batman. Actually, I wouldn't do it justice, just watch it here:
That episode is both one of my favorite pieces of Batman media ever, and also an excellent example of both a "lower decks" episode and a vignette episode. Absolute gem of the whole series.