April Ryan and Jade are some of the best videogame characters ever! Jade was seriously badass, not overly sexualized (though the model was pretty), cared about orphans and political realities, and decided to take on an oppressive regime. Seriously, how much more badass can you get than that?
As for Shepperd, well, she was badass in the sense of ultra-militaristic glorification of violence, i.e. not my cup of tea. If I was going to go for a kill-everyone-in-sight madness badass, I'd say Tiny Tina from Borderlands 2. Not someone I'd want at my side under any circumstances, but really, really badass (and scary).