This is a very tough one, my fave film and comic character versus my fave vid game character...
So let's look at it properly.
Link is just a boy - yes, until he reaches The Master Sword. He then ages by 7 years to become what, 19ish? Yeah he's still a boy but less so by this point.
This WILL be the closest of the battles but this comes ALL down to the armouring.
Link has Nayru's love, invincibility for a set amount of time in short. He also has Din's fire, which wraps himself in fire...
He has the masks also. But what happens if Batman uses the grappling hook to take away those masks? Turning into a goron would have little effect on Batman as Batman has his explosives which would EASILY destroy the rock armouring. Zora link would have twin boomerangs and could play guitar at batman but that's about it, and deku link would have little effect also. So this comes down to the mirror shield, the megaton hammer, and pegasus boots for link as well as the longshot.
I could see both men disarming one another continually, with grappling hook and longshot relatively.
This goes back and forth, but I THINK just due to the versatility and also some of the twilight princess powers, Batman would fall. I mean the gale boomerang here would have some effect, being able to create tornados which would sweep batman off his feet for instance. Dropping bats down hard would be a good start with one of those, a few deku nuts and then a few well timed stabs. Batmans armour is very strong though and would take a LOT of hits, but yet we've seen batman's armour beaten up more than once - IE, once it's beaten up and broken, it's bruce wayne we're looking at.
This is the thing. Batman is still bruce wayne, and once the armour is broken down, which fire arrows would do well with (setting wayne on fire), it's no longer batman that Link is facing. Link is ALWAYS link.
Not to mention the 4 fairies in bottles he'd have stacked away too
