One of my friends rented this, probably in later elementary school to early high school (late 1980s to mid 1990s). There was a tournament with monsters fighting. I don't remember if it was brackets or a ladder tournament. The graphics were 2D. The monsters, as I recall it, were largely quadrupedal, and fought in something like a boxing ring. I remember the fighting gameplay as being a bit clunky, I think involving moving around the ring with the D-Pad and being able to do attacks with the action buttons that might have only hit left or right. One of the features of the game was that, after a battle (I think maybe only if you won?), you could mix your monster with the one you fought, I think in a vat of chemicals, which caused you to gain some of their traits. As I recall it, this was not always a positive thing, with the mix sometimes leaving us with a monster that didn't do as well in the fights.
I don't remember a ton about the gameplay... I think I remember at least one of the monsters had a poisonous stinger tail (which we gained by blending the monster with their opponent after a fight). I don't recall if we made it to the end of the game, having found it less than satisfying to play despite the awesome premise of monsters fighting and being genetically blended with each other.