Like with other cosplays, the Catwoman costume is a perfect costume created by Lumina for Alexandra to become Catwoman.
Requiring an actual human appearance under the iconic catsuit, Alexandra must first be fully encased in the Skinsuit disguise, over which she then wears the actual Catwoman costume. It’s specifically made to fit with Alexandra’s extreme proportions. The catsuit is in fact one single piece of clothing, the only openings being the area around the mouth, eye holes, and a connection point between the legs for the maintenance port, so that Alexandra can also go through a full maintenance cycle without having to remove anything. This means to put on the catsuit, the mouth area has to be stretched wide open and Alexandra has to climb into the suit. This area is also specifically made to actually contract enough so that it cannot be stretched open again, trapping Alexandra inside the costume, until this area is opened up again by Lumina.
There are also various gadgets and iconic items Lumina and Alexandra have created that belong to Catwoman. Finally, like with other cosplays, Lumina engages a slightly altered version of Alexandra’s personality and character, making mental changes for Alexandra to become the ultimate fetish Catwoman.