Batman: The Animated Series is the first video game to be released based on the actual Batman animated series which was broadcast at the same time. It was only released for the Game Boy.
The game is an action-adventure platformer in which the player, for the most part, controls only Batman and controls him to the end of a stage where there is usually a boss waiting for him in the form of one of Batman's enemies from the animated series. However, the style and design of the stages themselves are different between each other, which gives notable diversity to the game.
There are a couple of occasions in the game in which control shifts over to Robin where you control him for a short time before moving back to controlling Batman.
Batman has some of his gadgets available which he can use such as his Grappling Hook and Batarangs. Robin can also use some of the gadgets too. In addition both characters have some abilities that they can individually use.
Source: Wikipedia, "Batman: The Animated Series (video game)," available under the CC-BY-SA License.