Here is the full list of all 15 Moustache Mountain achievements.
Reach Level 7!
Die within 2 seconds of starting a level!
Start a new game for the first time!
Reach the top without dying!
Reach the top of the mountain!
Die from all traps!
Successfully dodge 200 arrows!
Fall off the platforms!
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!