The name translates into "Bravo Tamagotchi! Rainboventure"
(with rainboventure being combined from words rainbow
This don't tell much but sure the name is cute.
If you dad knows japanese, ask him to translate the description of the game (the long japanese text)Official Page of the game
(the top advertisement is this Rainbow-adventure's. The advs in down left and right are Tamagotchi Corner Shop I and II advertises)