Taitos sequel to Bubble Bobble actually had very little to do with the original game. Single player only, the idea of the game was to travel through 7 worlds, each containing 4 rounds.

Each round consisted of a long verical level, which Bub had the reach the top of inside of a certain time limit, otherwise the water level started to rise, and if it wasn't outrun our hero would drown! To aid then in their quest Bub had the power of the rainbow, which can be used the walk and jump on, as well as to kill the abundant bad guys by smashing the rainbow whilst it was above the enemy, or by a direct hit.

To make thing a little more tricky at the end of each world you are confronted by the world boss, some of whom are exremely tough cookies.

Somewhat a rarity in the arcades nowadays (I've never seen it), it was recently(ish) released on the PC, PSX and Saturn which are the versions to buy if you want to play it now. Alternatively get the emulator RAINE and play the arcade version!