The name translates into
"Bravo Tamagotchi! Rainboventure" (with rainboventure being combined from words
rainbow and
adventure)
This don't tell much but sure the name is cute.
Jiro:
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)