Here is the full list of all 20 Pony Island achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Found the hidden profile screen.
Learned every secret of your past.
Learned a third secret of your past.
Found all 24 tickets.
Found Missingno.
Learned another secret of your past.
Learned a secret of your past.
Escaped the arcade.
Destroyed the third Core File.
Found 14 tickets.
Killed Louey.
Destroyed the second Core File.
Found an alternate avatar.
Unlocked Pony Wings.
Destroyed the first Core File.
Unlocked Pony Lasers.
Found 7 tickets.
Crashed the game.
Found 3 tickets.
Found your first ticket.