Is there some historical context about Ayanami being called Black Panther and Demon God? Am I missing out on something?

Her wiki entry in Danbooru says

She is termed the "demon goddess" of the Third Torpedo Division due to her performance in the Third Battle of the Solomon Sea, where she alone formed one 'prong' of a three-pronged attack. She assisted in the sinking of three destroyers (heavily damaging a fourth) and traded fire with a battleship (she severely damaged it, but was ultimately sunk in return).