The basic premise of the game is that each level is an island which is slowly sinking into the sea. The player must therefore get to the top of each level, by jumping on platforms and making use of the game's most distinctive feature: the ability to produce solid rainbows, which are used both as platforms to stand on, and as a weapon (remember the case in Bubble Bobble when using gum bubbles for the same reason!).
While initially appearing to be quite a simple game, Rainbow Islands in fact has a vast number of secrets for the player to discover, including secret levels, secret power-ups and riddles. Because of these elements, completing the game properly requires a large amount of dedication from the player. Note that the C64 ports runs way better compared to the Amstrad CPC and ZX Spectrum ports...
Both C64 and CPC versions feature excellent cartoon-style graphics, with great colors. Most of the detail is ported successfully from the (arcades) original version. The c64 version is better in terms of frame-rate. Sprites move fast and screen scrolling is fluid (in contrast to the CPC, ZX background scrolling which flickers). In terms of colors, the graphics look a bit better on the CPC though (due to the better color palette).
Soundwise, the C64 version offers the original superb soundtrack along with a few cute sound effects during gameplay.