Sorry, got the color of the gem in the pommel wrong.
So, like, Bekka's family is killed for some reason, like they're minor barons or something (it happens on Apokalips, I think Kanto is a baron as well), Bekka is put into Granny's orphanage and maybe is betrothed to Kalibak when she's older and properly processed into a Female Fury (can they have husbands?) when a former servant of her family who's still loyal manages to somehow break in and give her the sword (which is probably how he broke in, now that I think about it). He/she gets killed in the process...or, better yet, they survive (it could be funny to give her an alien Alfred/Aunt Harriet to watch over her) and both of them Boom Tube randomly to escape and end up on Earth.
I figger she's a bit of a priss because it's the only way she can process how fucked up her life got in such a quick time, so she and Damian tend to butt heads (she doesn't take his shit, he can't physically harm or intimidate her) despite Jonathan totally crushing on her (of course she doesn't notice at first), and she fixates on Wonder Woman because she's the most prominent and powerful female hero in the current DCU, which is why she takes a uniform similar to hers.
Throw in Iris "Impulse" West, escaped fromt he Flashpoint rewrite due to Flash powers being immune to continuity rewrites, we got a new pre-Teen Titans...I guess just call them "Young Justice," then.