The SNES version is developed and published by Konami. Each level consists of an episode that is loosely based on those from the animated series, taking Batman to an amusement park and other places where super criminals do their nasty work. Nintendo Power criticized the game for not giving Robin a more active role (although the game was actually under development before the series was retitled between seasons). Otherwise, he supplies Batman with his moral support. Despite this, the game was well received by fans and critics citing the faithful rendition of not only the characters and settings but also the music of the actual animated series.
Source: Wikipedia, "The Adventures of Batman & Robin (video game)," available under the CC-BY-SA License.