Here is the full list of all 27 Default Dan achievements.
Defeat the Cupcake King.
Obtain 5 stars collectively from stage rankings.
Complete Level 4 without killing any enemies.
Complete Level 1 without jumping more than 3 times.
Obtain a 3 star ranking for Level 7.
Complete Level 8 without dying.
Complete Level 9 without touching any checkpoint flags.
Complete Level 10 while on fire.
Obtain a 3 star ranking for Level 13.
Complete Level 15 without killing any enemies.
Complete Level 17 without jumping more than 4 times.
Defeat the Princess.
Complete Dark World.
Achieve 100% Completion.
Obtain 7 stars collectively from bonus stage rankings.
Collect 10 dynamite.
Collect 25 dynamite.
Collect 50 dynamite.
Obtain 20 stars collectively from stage rankings.
Collect 30 coins in a single death. Bonus stages don't count!
Kill 30 enemies with fire in one run.
Collect the only collectible coin.
Woot.
Fall at terminal velocity for 10 seconds.
Die 30 times in a single stage or boss.
Kill a bouncing heart while standing on a springboard.
Collect 1000 coins.