Puzzle Fighter, is that you? Capcom Quest of Felyne Puzzle! A Tetris Monster Hunter.
Another one that would definitely be a mobile game nowadays, haha
It was probably on purpose, Felyne Puzzle's mechanics are identical to Super Puzzle Fighter II. The only difference I noticed is the possibility of rescuing the egg that destroys any block after you fill the bar.
Of course, you can customize your "Palico" well in addition to unlocking several others!
it's very quick to beat the story mode, even with two rounds to defeat the enemy, haha.