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