Essentially the player takes on nearly exactly the same type of side scrolling action found in the NES game, with similar but simplified graphics and enemies. It is only a single player game and starts out in a level similar to the NES game as well. The task is also similar, with the player playing as Zitz having to rescue both of his partners, Rash and Pimple.
However, there are plenty of differences in the levels and range in difficulty when encountering enemies or obstacles. The same "over-the-top" finishing combos can also be found in the Game Boy release.
As in the case of the original NES game, the Game Boy game is also notoriously difficult to beat, requiring fast reflexes, memorization of obstacles, and patience.
Source: Wikipedia, "Battletoads (Game Boy)", available under the CC-BY-SA License.