Here is the full list of all 21 Button Tales achievements.
Complete 3 levels without power-ups
Use the Hammer power-up
Complete a level without swaps (flips only)
Complete a level without flips (swaps only)
Remove 20 buttons in one move
Complete a level in a minute
Use the Yarn power-up
Use the Lightning power-up
Use the Acid power-up
Use the Scissors power-up
Use the Brush power-up
Make a match with 3 pins
Make 5 matches with buttons of the same color
Complete 20 levels in one session
Use all the power-ups in the same level
Make 20 or more matches of 4 in a row
Remove 3 or more jewels in one move
Earn 15,000 gold in a level
Repair all buildings
Match 8 or more buttons
Earn all achievements