Superheroes again, she wasn't surprised. She gave a quick nod, but then looked at her funny. "You trained me?" she asked in disbelief. This woman had to either be insane, or a lot stronger than she looked. "I'm going to have to assume you're not very breakable then." because what other way would Kara have not killed someone through training? Even if someone had powers, all she had to do was bump into someone hard enough to knock them out. Diana must have known how to take a hit then. That or Kara went really easy on her.
Kara eyed the woman slightly. She had a discussion with Bruce Wayne, in private, who had called himself Batman. Since then, he had vanished for a while from the boards, and then re-appeared. If this was the same Bruce, she didn't now. "He called himself Batman." she said with a shrug. That wasn't giving Bruce away, and if Diana really knew a bunch of superheroes, she would know who that was, wouldn't she? It made sense in Kara's mind anyway. "He also mentioned someone named the Joker. On top of that, there's some guy here who made reference to 'Superman,' and something about him being a hero." last she checked, some people seemed to think Clark was Superman...at least when he had powers. A few people who had known Superman also mentioned Supergirl, which was apparently her.
"From what I gather, Clark and I are supposed to have capes and code names in other realities. I can't say either of do that here, though I think my cousin might have been considering it." it would be dangerous though. How would people not recognize him? It didn't make much sense to Kara. It seemed like it could be fun, but with all the things happening here, and then sun being blocked, it would be a while before anything like that happened.