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