Here is the full list of all 12 Black Rainbow Mystery achievements.
Find 7 Special items
Solve 5 Minigames without using Skip
You've solved 1 Minigame without using Skip!
Find 1 Special item
You've finished the game (any mode except Challenge)!
You've finished the game in Challenge mode!
You've finished the game without using any Hints!
You've finished the game without using Skip (and solved all of the minigames)!
Solve 10 Minigames without using Skip
Find 14 Special items
Find 21 Special items
Finish the game without skipping any dialog