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