Here is the full list of all 14 Ponpu achievements.
Beat the third boss
Beat the second boss
Collect 100 feathers
Beat the first boss
Collect 20 feathers
Finish the tutorial
Beat the fourth boss
Beat the fifth boss
Complete Story mode
Win 1 online match
Win 5 online matches
Win 10 online matches
Collect 500 feathers
Unlock all the achievements