The Three Beauties were introduced as these special patients in Arkham Asylum that neither the staff nor the inmates were aware of. They were locked in a solitary confinement chamber that only the former Arkham Director, Jeremiah Arkham, had access to. The members consisted of:
Born Alessio Morandi, No-Face disfigured himself by gluing a mask to his face when he was a child. His personality was destroyed along with his features until Jeremiah taught him to express himself through the blank canvas on his face.
An enigma to himself and to others, Mirror Man was a man with no name and no past. He was pathologically obsessed with himself, unable to use language except by echoing phrases spoken by others. Jeremiah called him Narcissus.
Myrna Freud was believed to have a face so disfigured and hideous that anyone who looked upon at her would be driven mad. Although she preferred to be left alone, she was happy being in the company of No-Face and the Mirror Man.
Jeremiah considered them as unique patients and became attached to them. The Beauties were the only ones who could relate to Jeremiah's problems and would comfort him in his time of need. When Black Mask took over Arkham Asylum and burned it to the ground, Jeremiah rushed to the Three Beauties' chamber and was relieved to see them alive and unharmed. They were then transferred to the newly-rebuild Arkham and were placed in an isolation chamber once more that only Jeremiah was allowed to enter.
The Actual Truth
During the events of Jeremiah pleading guilty of impersonating the Black Mask, Batman interrogated him and said that he had never cured a patient in his lifetime. Jeremiah proved him wrong by telling him about the three patients that neither Batman nor Aaron Cash were aware of. This was when Jeremiah first revealed the existence of the Three Beauties to anyone.
It was finally revealed that there never was Three Beauties and that they only exist in Jeremiah's twisted mind. This was proven when Batman and Cash followed Jeremiah to the isolation chamber and witnessed the former director talking to himself and hallucinating. Cash did an investigation beforehand and found out that the asylum hold no records of these Beauties and no evidence of anyone seeing them before. Under further investigation, the hallucination came to be when Jeremiah inhaled a Joker Toxin that was encapsulated in a harlequin toy that was given by the Joker himself. Jeremiah had the toy in possession since then and was not aware that he had been inhaling the toxic fume this whole time. The Joker toxin began to effect his mind and that was when the hallucination began.