Depends which Shredder we're talking about. Shredder from the first TMNT movie had some insane martial arts skills, with none of the turtles lasting more than a few seconds with him.
I say Shredder beats Batman after a pretty good fight, considering ofcourse that Batman doesn't get to bring in his advanced tech to the fight. Otherwise, he'll just throw knockout gas at Shredder (which I don't know why he didn't do to Bane btw).
As for super Shredder in TMNT2 well... if Bats had problems taking down a powerful brawler like Bane, super Shredder will decimate him. Again, only if it's h2h though.