User summary from Japanese Wikipedia:
Parasol Stars was an action game released in 1991 for the PC Engine (TurboGraphx). It carried the subtitle "The Story of Bubble Bobble III" and was thus the sequel to "Rainbow Islands" (The story of Bubble Bobble II), but like its predecessor, it did not share game play with Bubble Bobble. It is currently available through the Wii Virtual Console as Parasolstars.
Like Bubble Bobble, the game consists of screens on which the players are supposed to defeat all enemies, in this game using parasols."
Source: Wikipedia, "パラソルスター," available under the CC-BY-SA License.