I'm definitely not the first person to point out the number of super villains with advanced degrees, but early Batman is such a great example of the trope.
There are eleven Batman antagonists that appear two or more times during the Golden Age. Dr. Death, The Monk, Dr. Hugo Strange, Clayface, Dr. Matthew Thorne, Two-Face, Tweedle Dee & Tweedle Dum, Scarecrow (Dr. Jonathan Crane), Catwoman, Penguin, and the Joker.
Of the eleven, four of them are Ph.D.'s or M.D.'s, (and one is a Lawyer). In 1940 less than five percent of the population had a four year college degree, in the golden ages about 45% of Batman's enemies had advanced degrees.