Nekketsu Oyako is a beat ’em up also known as Thermal Blood Parent and Child or Hot Blooded Family. The game was released for the Playstation in December 1994 and for the Sega Saturn in July 1995.
On an interesting side note, the game’s first level ends with the player being swallowed whole by a giant whale. The “belly of the beast” trope was listed in a recent GamesRadar article entitled Myth in games.
Click past the break for direct feed footage of the first two stages with Rio selected as the player character.