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