Parasol Stars was released in 1991 and it is a sequel to Rainbow Islands.  In other words, this game is technically the third game in the Bubble Bobble series.

In the game, Bubby and Bobby are the main characters.  The action takes place on various worlds, each with a distinct theme.  A boss must be defeated at the end of each world and the player has to unlock two secret areas in order to properly finish the game.  Your main weapon is a parasol which can be used in various ways:  as a shield, to stun enemies, as a parachute, to capture droplet, or to hurl enemies.

This game did not see a lot of ports and may not be as known.  It was certainly an unknown for me!  So, here is the video comparison...

https://youtu.be/_D6euvpJ7gY