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.
Learned every secret of your past.
Learned a third secret of your past.
Learned another secret of your past.
Learned a secret of your past.
Escaped the arcade.
Destroyed the third Core File.
Found all 24 tickets.
Killed Louey.
Destroyed the second Core File.
Found Missingno.
Found an alternate avatar.
Found 14 tickets.
Unlocked Pony Wings.
Found the hidden profile screen.
Destroyed the first Core File.
Unlocked Pony Lasers.
Found 7 tickets.
Crashed the game.
Found 3 tickets.
Found your first ticket.