Here is the full list of all 27 Default Dan achievements.
Die 30 times in a single stage or boss.
Defeat the Cupcake King.
Obtain 5 stars collectively from stage rankings.
Collect the only collectible coin.
Woot.
Complete Level 1 without jumping more than 3 times.
Complete Level 4 without killing any enemies.
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.
Fall at terminal velocity for 10 seconds.
Kill a bouncing heart while standing on a springboard.
Collect 1000 coins.