Never saw this on the site and its highly worth bringing up.
Supergirl: We Don't Need Another Hero is a point and click adventure game a fan made a several years ago.
www.adventuregamestudio.co.uk/site/games/game/505/
Not sure if when you think superheroine you think point and click adventure, but actually it does kind of fit-most superhero comics play feel more like adventure games then any kind of action ones-and it does a pretty good job with a lot of the tropes and ideas of an ubergirl, and encorporates her powers and her strength pretty well in spots. I might argue that its one of the better superhero games i have ever played in that regard. It feels like your playing a comicbook which is something i don't get from Arhkam city.
Its also funny in parts or at least smiling. This isn't like sam and max or adventures of monkey island in terms of humor, but it creates its premise-that someone else is named supergirl and the real one has to fight to clear her name pretty well. At its best it does a good job of suggesting someone who is not used to exasberation. The games creator has a good sence of the kind of slightly angsty linda danvers.
Its about an hour. It was made in 2005 and the graphics weren't top of the line then, but its fun if you let it be. Its also free and worth playing if you want to.
Castor