As Robin finds out about the Mafia, he discovers that Tony Zucco was present when Dick's family was murdered, which worries Batman.
Then, Robin finds Tony Zucco and Batman follows suit.
It was when Tony Zucco murdered Dick's family, which led him to become Robin. Then, Batman and Robin encounter the Joker again and apprehend Zucco, but Joker gets away.
After this, Robin decides to leave Gotham to prevent those from suffering like him, and Batman wishes him good luck.