User summary (details from Japanese Wikipedia):
An arcade shooting game from 1990, developped by Konami. It's the sequel to "Parodius" for the MSX in 1988.
Parodius da! is a typical "cute'em-up", a shoot'em-up with a cute bubbly fantasy theme. It's based as a parody of Gradius and follows the same game system, borrowing some essences from the cute'em-up Twinbee.
The arcade was so popular that the game was ported to an astonishing number of platforms, from the Famicon in 1990 to the PSP in 2007.
Source: Wikipedia, "パロディウスだ!_〜神話からお笑いへ〜," available under the CC-BY-SA License.