Amelia Wayne wasn't quite sure when she actually stopped caring about what the media thought of her. All she remembered was that she just did at one point.
After all, the media was very likely to lie about her and her siblings anyway, do why would she even care anymore?
Nobody was really interested in the actual truth about the Wayne kids anyway but instead the started to create their own truth, built on nothing but lies, half truths and weird assumptions that were based on blurred photos and audio clips, where one couldn't be sure if it was actually one of the Wayne kids speaking or just someone who was really good at imitating voices.
So why should Amelia always defend herself when nothing she said changed anything about the things that the media said about her?
In the end it was just a waste of her energy, energy that she actually needed for things that were way more important. Like fighting the crime in Gotham City that seemed to never end or trying to keep up that carefully build facade of hers.
She even hated the thought of being just as vulnerable as she was after the day day Jason was killed. Even though she tries to forgot what exactly happened that day, she still remembers the pain and how she broke down crying on the stairs of Wayne Manor after she found out what happened to the brother that was closest to her.
She remembers being really alone for the first time.
Her mom was locked up in Arkham again, her dad was dealing with his own demons and guilt and Dick was nowhere to be found since he moved out after a fight with Bruce.
And even though Alfred tried to be there for Bruce and Amelia it was obvious that it was hard for him and he also felt some sort of guilt about all the things that happened.
And during one of the darkest days of her life Amelia Wayne promised to herself that she would become a better and less vulnerable version of herself. A girl to whose strength and elegance others would look up to, some sort of role model.
And around a year later, when Tim Drake became Robin and her mother was released from Arkham, she also started to train and took on the mantle of Catgirl.
As Catgirl she wore a mask and she failed to realize that it was hard for her to take off that mask, even when she was just Amelia Wayne.
Maybe it was around this time that she stopped caring about the media and it's picture of her or maybe it was just the beginning of this mindset.
But she knew that by the time Jason was back from the dead and Barbara was shot in the back by the Joker she stopped showing any emotions towards the outside world which lead to the nickname "Ice Queen".
Amelia Wayne was actually nothing more than a broken girl, trying to hide her true self under several masks and empty relationships, scared to be hurt and lonely again.