Here is the full list of all 15 Moustache Mountain achievements.
Reach the top without dying!
Reach the top of the mountain!
Reach Level 7!
Die from all traps!
Successfully dodge 200 arrows!
Fall off the platforms!
Start a new game for the first time!
Start a new game 10 times!
Start a new game 50 times!
Start a new game 100 times!
Complete the game in under 5 minutes!
Complete the game in under 4 minutes!
Finish the game in under 3 minutes!
Die on the last level!
Die within 2 seconds of starting a level!