Teenage Mutant Ninja Turtles II: Back From the Sewers is a licensed brawler/action platformer hybrid from Konami made exclusively for the Game Boy. Although the majority of the game is an action platformer, there are several brawler segments. Its combat is straightforward yet requires precise timing, and you can play as all four turtles (each of which counts as a life.) If you lose a turtle, you have the chance to fight a guard to free them so you can play as them again.
The first 'Turtles Game Boy game was a pure action platformer with no brawler segments. The third one is a Metroid-style exploratory action platformer where each turtle has a unique ability that's needed to proceed (for example, Michaelangelo can spin his nunchaku to float in the air and Donatello can climb walls.
To execute the slide attack, press A + B simultaneously. This works in both brawler and platformer segments but not during vehicle stages.
Back from the Sewers was one of my favorite games as a kid. Although it has little actual brawler combat, its action is always tight and can be fairly tricky on the hardest difficulty setting. The graphics and sound are some of the best ever seen on the Game Boy and it's full of beloved Turtles characters and settings.