In those comics, she was “Kathy Kane” (presumably, after Batman creator Bob Kane) – but here she is bored heiress turned thrill-seeker, “Katrina Moldoff”.
Katrina (somewhat recklessly) assists in the capture of The Riddler – but not before she becomes careless and allows The Prince of Puzzlers to UNMASK her before a crowd of onlookers and reporters… to her shock, horror, and utter humiliation. Clearly, she is known as something of a public figure or celebrity.
We shift forward, ten years to “The Present”:
Twisted by her anger, she seeks the assistance of FELIX FAUST – the sorcerer from Silver Age “Justice League of America” comics, who has served his time and is quietly operating a sorcery shoppe somewhere in the nether regions of Gotham.
Faust is quite taken with the still-slinky Katrina, and provides her with a potion and incantation that will allow her to (…Ready for this?) SWITCH BODIES with the person of her choice. She lures Batman to her remote mansion and does exactly that, overpowering him in the process!
Things take a real turn when they learn that Katrina (as Batman) plans to kill The Riddler for his decade-old deeds, and have Batman appear to be the killer. Batman comes-to, dons Katrina’s old Batwoman suit, and goes after her. Big bouts of Bat-gender-bending ensue – with “he as she” and “she as he”!