Here is the full list of all 18 HatMania achievements.
Complete the final level
Collect every coin
Complete every time trial
Complete every level
Complete the game without dying
Collect the coin and complete the time trial in the same run in any level
Complete level 50 with a time of 5 minutes or more
Complete a level 1 second faster than the target time
Die 10 times on the left side
Die 10 times on the right side
Die 100 times on the left side
Die 100 times on the right side
Die 1000 times on the left side
Die 1000 times on the right side
Complete a level 3 seconds faster than the target time
Complete a level 5 seconds faster than the target time
Complete the game while dying less than 10 times
Complete the game while dying less than 100 times