Here is the full list of all 10 Rainbow Hunter achievements.
Complete all levels
Do a higher score starting level 10
Complete all the first 20 levels
Get the fairy item in the 10 first levels
Get the boot item in 5 different levels
Arrest the Leprechaun in the cage in 5 different levels
Get at least two items in rain level
Complete a snowing level with the Leprechaun in the cage
Complete 40 levels