In the spirit of full disclosure, The Adventures of Batman was not truly the first animated appearance by The Cowled One, Batman nor the pixie-booted Robin. The animated Duo first hit the airwaves during the opening credits sequence of the live-action Batman series beginning in 1966.
Introducing Batman and Robin, the opening sequence also offered up quick cameos of the Joker, Penguin, and Catwoman.
Of course, the duo make quick work of the baddies and call it a day, all in under a minute. See for yourself:
For fun, here is an updated fan version inspired by The Dark Knight:
and with Legos