Found this in a review. It's the final boss in Bebe's Kids, which was a terrible game. I don't mind the game itself, but at the time I only had a small collection of SNES games. This was one of them. Somehow, I managed to complete the game including defeating this boss.
This boss is terrible. It's attacks are lame, the weak point is difficult to hit, and it's bullshit annoying. Hell, the enemies in Streets of Rage III were bullshit annoying, but this was ridiculous.
I didn't play the game a second time after completing it, mostly because Streets of Rage II was available and was about 80 times better. There was also The Simpsons at my local arcade, which I didn't enjoy half as much as the SoR series but at least it wasn't
Bebe's Kids.
Jam it back in, in the dark.