Scenario One:The TMNT invade Batman's Batcave, It is a fight to the death and batman gets no prep time,Who Wins?
Depends a lot on which generation of Batman and which generation of turtles. Batman movie Batman or Justice League Batman? 1960s Adam West Batman? Adam West would be absolutely slaughtered by any one of the turtles. Or do you mean comic book batman bench pressing 1000 pounds and surviving the vacuum of space because he's just that tough and able to go toe-to-toe with divine super beings? TMNT 1990 movie turtles or 80's back and white comic turtles? It makes a big difference.
I'll assume Michael Keaton / Christian Bale Batman vs 1990 movie / 80s animated turtles.
If it's
genuinely no prep time, four turtles burst into his cave, he's not even wearing his suit, and it's
genuinely to the death, I think the turtles win. Four on one, very probably physically superior and more durable, Donatello keeps him on his toes while Leo cuts him down. Raphael gets caught by some batcave defense and Michaelangelo gets himself stuck in some silly batcave contrivance that
isn't a trap, but lives. If Bruce has his suit, he lasts a lot longer, but he has to play defensive and how long the fight lasts depends purely on how long it takes Leonardo to listen to Donatello shouting at him to aim for the face.
But it wouldn't play out that way. Bats would realize it was bad situation long before Leonardo started listening to Donatello, and would simply abandon the fight to gather more information. The turtles wouldn't be able to stop him from escaping. Further, stealth are infiltration aren't things that Team Turtle are especially good at. There's no way they'd make it into the cave, even onto the estate without tripping an alarm or showing up on a security monitor. Bats would know they were coming. He'd be ready and his defenses would be ready. Michaelangelo would waltz right into them, Raphael would get angry, Leo would be too caught up trying to be the good, selfless leader to keep himself out of trouble and Donatello would be the only one keeping his head on straight. They would be netted and gassed before they ever made it inside.
Further, Batman would be
very unlikely to push the battle to the death. The turtles are very outspoken, and he'd figure out pretty quickly that the whole thing was some sort of silly mistake. Leo is also very reasonable. Bats would quickly identify him as their leader and tell him "I'm not your enemy." Leo would object, but Bats would persevere, and eventually he'd listen. They'd all talk it over. Raphael would get angry, Michaelangelo would meet Alfred, be introduced to hors d'oeuvres, mispronounce the name and then proceed to eat a bunch while cracking jokes. Donatello would be thrilled with all the wonderful toys and Bats would quickly realize they'd make good allies.
But yeah, four turtles materialize into the batcave on top of an unprepared Bruce Wayne/Batman, no-nonsense brawl to the death, no retreat or parlay allowed, Batman loses.