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