Alright, I'm not gonna go into depth, but I'll give a bit of info of both sides:

Batman --

Master Martial Artist (Best Ever, mastered every martial art in existance)

Genius Level Intelligence

Master Tactician

Master Strategist

Can lift up to 1500 lbs

His speed and reflexes are practically superhuman

Master Ninja

Definitely has more experience

Turtles --

Hard Shells to protect from attacks

Specialize in Ninjutsu

Are expert ninjas

Master Splinter --

Master in Ninjutsu

Expert Ninja (You don't find him sneaking around often..)

Specialized in tactics

These ninjas apparently can't fight without weapons

Scenario --

Batman is patrolling Gotham, he sees some weird ninja figures jumping about rooftops. He assumes they are the League and goes in for a surprise attack. As he closes in, they're.... turtles? Batman is wondering who they are and who they are affiliated with. He follows them, he analyzes them, he notices they're not all that good in team-work, judging by their voices, they're just kids (Not literal kids). He also notices their shells, if they're a threat, he needs to be able to break them. Batman just drops down right in front of them, startling the turtles. Intimidating Mikey instantly, Leonardo is alerted, Raphael is alerted, donatello is nervous. This dark shadow figure in front of them is mysterious. Leonardo gently says "We don't want any trouble, where are we anyway?" Batman sits in silence for a while and says "Gotham. Get out of my city." Raph yells "Don't talk to my brother like that!" Batman is in front of Raphael's face within seconds staring him down 3 inches away. Donatello takes a swing at batman but batman grabs his staff with one hand and throws it and dropkicks Don. Raph goes in to stab batman but batman dis-arms him and gives him two swift-kicks to the face, throws raph's swords at mikey as mikey is charging in and tosses mikey across the roof while he was distracted by the swords. Leo doesn't take too kindly to people messing with his brothers. While batman's fighting, leo throws one sword, and jumps above batman, batman blocks his sword and dodges his attack then taunts "You didn't think I forgot there were four of you, did you?" The turtles quickly regroup a safe distance away from batman, watching him, but planning an attack. Batman's just looking, analyzing and taking what he learned from their encounter and realizes, they're not all that good. Leo says to the group "Alright, this guy is ridiculous! We didn't even touch him!" Mikey says "Yeah, at least we actually hit shredder.". Ralph argues "This punk just got lucky! I bet he's with shredder!" Don just listens and keeps a close eye on batman. While Don watches, he doesn't see anything but a dark shadow figure, he literally sees nothing but a bat figure with white glowing eyes. Don literally, right before his eyes see that shadow figure vanish quickly, he saw the direction but he lost track. Don alerts everyone they he's moved and they go into that turtle circle form.

Batman isn't fighting them. He just says "Get out of my city, or I'll make you. And tell your master too." Leo shout "This isn't your city! You're working with shredder! You're another villain!". Mikey adds in "How do you know we have a master?!" Batman's says "I didn't. You just told me." Ralph punts Mikey in the head and says "WILL YOU SHUT IT NEXT TIME?!" Mikey screeches "Ow! Hey, I thought he knew, okay?!" The turtles turn to Leo but, Leo's gone. Leo thinks I need to find this guy, he may even be better than shredder. Leo spots batman walking on a rooftop. Batman knows he's there. Leo tries to creep on him but batman says "Don't try it. Leo." Leo feels insulted. Batman calling him Leo like he knows him? He grunts "JUST WHO THE HELL ARE YOU ANYWAY?!" .... "I'm batman.." Leo's curious and asks him "Did Shredder send you?!" Batman just turns and says "I don't work for anyone. This is my city. You've got a day to get out of it." Leo attacks batman for being so ignorant, batman dodges his attacks, grabs his sword and knees Leo in the face. Batman warns "You've got a day. After that, I'll let robin deal with you.". Jumps off a roof, when leo looks, the bat vanished.

Leo rushes back to the group and they're all up-tight about him leaving complaining "Why'd you leave dude? Where'd you go?!"..."I went to face batman"...The group gasps, Raph anxiously asks "Did you win?"..."No. He's better than us. We need splinter."...Mikey butts in "But splinter only wants us to contact him in emergencies!"...."And this isn't an emergency Mikey?". The group goes cold with silence. And they go into the sewers searching for splinter. "I don't recognize any of this" Donatello says. "Maybe the shadow-freak is right, we might be in his town." Raph is intrigued by all this and says "Maybe we shouldn't have went to sleep during our train ride"(They were not IN the train, they hitched a ride on top). After a few hours of searching, the turtles finds splinter and brings him to "Gotham". The turtles flooded him with details and advise splinter should be careful.

Splinter and batman meets on a roof, they fight it out. Batman is way too fast and strong for splinter, but batman's tripped and kicked by splinters tail. Splinter wonders if batman is even human judging by his speed and reaction time. Countering and dodging almost every blow. Batman's winning and the turtles charge in, giving batman more of a problem. Splinter throws a punch but batman grabs his fist and bends it backwards while blocking raph's attack with his other arm. Mikey goes in to choke batman with his nun-chucks but batman jumps and kicks him, Raph tries to tackle batman but batman jumps over him and is 3 inches from Leo's face. Batman tried to punch Leo in the stomache but... he's a turtle.. leo then kicks batman, but batman still barely blocked. Don swings his stick in crazy ways, batman dodged and tripped him. Splinter came from behind batman and started to drop combos off guard. Batman is on edge fighting these 5. Batman drops smoke bombs... silence. Mikey screamed, Batman stomps on splinter's tail, pulls it then tossed splinter across the roof, Leo tried to leave the smoke but ran into batman's armored chest. Batman picked Leo up by the neck and threw him. Batman left Don though.When the smoke cleared, Mikey was hanging up-side down behind batman knocked out. Raph was knocked out on the edge of the roof. Now it was 3 v 1. Splinter knows he can't do this and asks for his "sons" back and he will leave. Batman backs up enough for him to get his sons. Splinter just asks 1 more question. "You're not a villain, don't know shredder and you protect this city, don't you?" Batman nods. Splinter just quietly walks out with his sons, telling them they need to train more.

Ok, I didn't try my hardest 100% on this. It was made at 11:00 at night. But it's pretty much the gist that batman would win. More experienced, better, faster, stronger, smarter. Their armor is probably just better than batman's. That's it.