Nightwing was able to hold his own for awhile against Deathstroke. If Nightwing could last a while then Shiva would dismantle Deathstroke (if it is hand to hand combat).
Hand-to-hand, maybe, even considering Deathstroke's enhanced abilities. But then again, with all firepower he carries, I doubt Shiva could stand against that. And back to hand-to-hand, most of us still remember Batman getting beat into the concrete by Slade.
True. Shiva would win if it was hand to hand combat. The only person who can give her trouble is Batgirl (and obviously characters like Karate Kid would be out of her league). But in 'everyday DC' Shiva and Batgirl are the greatest.
However if this was an anything goes fight Deathstroke would win. He would be too bright to dare face Shiva Woosan face to face.
Same thing goes for Batman. He would get his behind handed to him by Shiva if they ever went hand to hand, but Bruce would never allow that to happen. He'd hit her in a different way that maximizes his own strengths and negates hers.