Parasol Stars, also known as Parasol Stars: The Story of Rainbow Islands II - or if you prefer, The Story of Bubble Bobble III - is an arcade by Taito. The title is quite strange because there was no "Story of Bubble Bobble I". Anyway, the game is the sequel to Rainbow Island, which was created and released by Taito in 1991.
Unlike its predecessors, Parasol Stars was not developed as a coin-op; it was released on the PC-Engine. The Amiga and Atari ST were the only computer conversions; they were published by Ocean in 1992. The C64 port was never completed. It's not clear if Taito was going to release a coin-op or not. What we know is that Parasol Stars is one of the most addictive, fun, and colorful platformers ever created. The computer ports, developed by Mick West, are excellent. The playability is perfect, the controls responsive, and the graphics are fantastic. I am personally a huge fan of Bubble Bobble, but Parasol Stars is even better. Of course, playing with a friend is almost mandatory because this is "co-op" at its best.
Oh, did I mention that the soundtrack is the famous "Lambada"? If this won't convince you to try it, I don't know what could do it.