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I'v heard marvelous things about Deathstroke, but can he take on the martial arts prodigy Cassandra Cain?

Debate.

I dont know, Batgirl jumped him once and made him look bad.
He was on a mission and she got in his way so he left.
Some people call that a win, I dont.

In a h2h battle to the end, no weapons.

DS would eventually tire Batgirl out, due to his healing factor that prevents the accumulation of lactic acid, he would simply outlast her.

Not to say he isnt a great fighter, but Batgirl is Batgirl, she could beat batman in h2h.
DS could keep up with her and definatly could get some awesome shots in but the best way would be to just outlast her, then kill her.

Batgirl #64 Deathstroke is supposed to really let loose on her.
May issue.