I don't know much about Shiva's history, except that she is the greatest martial artist in the DC Universe.
Batgirl was raised by her assassin father Cain to be an unstoppable killing machine. She never learned to speak, only to fight. She can counter any move because of her ability to read body langauge perfectly. During "No Man's Land" she joined the Batman family as Batgirl. In one of the early issues of her series, she met a telepathic guy of some sort who unlocked something in her brain that finally enabled her able to speak. Unfortunately, doing that also made her lose the ability to read body language, and she wasn't nearly as good a fighter as before. Later she met up with Lady Shiva, who did something (they never said what) that gave Batgirl her fighting ability back, on the condition that they would have a fight to the death 1 year later. Batgirl doesn't stand a chance, so it'll be interesting to see what happens.