Here is the full list of all 11 Handsome Mr. Frog achievements.
Break 100,000 points
Clear the Spooky World and loop!
Clear the Construction World
Clear the Ice World
Break 50,000 points
Clear the Swamp World
Collect your first hat
Collect 10 hats
Collect 50 hats
Eat 50 Chili Peppers
Break 250,000 points