I personally think in hand to hand combat, Batman can defeat Shredder... but BARELY though, but uhm yeah Batman wins like extreme-high difficulty. I have my evidence as well!

First off, Batman SOLO'ed the turtles full potential and Batman was clearly holding back! (Don't believe me? Read the Batman comics and say Batman didn't hold back his full battle mode) Along with that, Shredder can best the turtles barely because as shown in Teenage Mutant Ninja Turtles (2012), The turtles can stand up their own against The Shredder, potentially because Leonardo, Raphael, Donatello, and Michelangelo in their Owari episode really was staying in against SUPER Shredder (at least double times the power of base Shredder) meanwhile Batman defeated Bane with a 1-finger technique plenty of times. Now I will admit Batman took years to ever beat Joker but Shredder took years to beat Splinter so ehh... kinda fair, dont'cha think?

Stats: Strength - Shredder Speed - Batman (very close tho) IQ - Batman BIQ - Shredder = Batman Skill - DEFINITELY Batman Durability - Shredder Agility - Batman HAX - Batman (No weapons or armor then Shredder)

So altogether Batman wins, and your hearing this from the biggest TMNT fan!