Save at the statue in the outdoor area. Start BiT. BiTWW using the lower (or upper) academy bird statue. Go to the Dark Lizalfos and whip him so that he get stunned, attack him one, spin attack and then do a finishing blow. Trying to defeat him normally will cause him to reset and block all your attacks because you haven't triggered the battle against him yet (it starts with a cutscene normally). Then enter the door.