Here is the full list of all 20 Happy Puzzle achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Complete 70 levels.
Complete 65 levels.
Complete 60 levels.
Complete 55 levels.
Completed the wizzard story.
Completed the queen story.
Complete 50 levels.
Complete 45 levels.
Complete 40 levels.
Complete 35 levels.
Complete 30 levels.
Completed Miko story.
Complete 25 levels.
Complete 20 levels.
Completed Caitlyn story.
Completed Eve story.
Complete 15 levels.
Complete 10 levels.
Completed Alicia story.
Completed 5 levels.