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