Ok, here's my analysis. I'm pairing them off after their placement on the pic. There's some people here I don't know who they are so they will probably lose.
Round 1Batman vs. Hit Girl They are similar, but one is an adult and one is a kid... Sure Batman won't kill Hit Girl, but he'd incapacitate her and then she gets eaten by a veliciraptor or something.
Winner: BatmanIndiana Jones vs. Eowyn Eowyn waves her sword around, Indy shoots her.
Winner: Indiana JonesRambo vs. Some chick with those triple blade thingies Don't know what she can do but Jurassic Park is a jungle which gives Rambo a big home team bonus.
Winner: RamboBear Grylls vs. Ripley Do I need to explain this one?
Winner: RipleyWilliam Wallace vs. Black Widow William can fight good but Black Widow has superstrength, superagility, superstamina...
Winner: Black WidowSome gladiator dude vs. Beatrix Kiddo Tough one. Gladiator type battles are exactly what The Bride does. I'll go with Natalya's reasoning on this.
Winner: Some gladiator dudeSome Game of Thrones dude vs. Xena Look at that guy. Seriously, he's leaning on his sword.
Winner: XenaHawkeye vs. Alice Hawkeye can... shoot a bow really good. Alice has a virus that gives her new powers as the plot demands.
Winner: AliceAragorn vs. Lara Croft Wow, more Lord of the Rings characters getting killed by bullets.
Winner: Lara CroftLeonidas vs. Katniss Everdeen Kids really should stay on the Battle Royale island.
Winner: LeonidasConan the Barbarian vs. Some black and white chick Can't judge this fairly because I don't know who that is. But I know Conan is a great guy.
Winner: Conan the BarbarianAchilles vs. Sarah Connor Sarah Connor seems to be a reasonably educated woman, she would know to shoot him in the heel.
Winner: Sarah ConnorRound 2Batman vs. Indiana Jones Batman would beat Indiana Jones up and move on. But when the veliciraptors come to eat Indy he'd get up at the last moment, get chased by them, and run right into a herd of sauropods. The sauropods get frightened by the raptors, stampede, smash down the trees Batman was jumping through, and crush him.
Winner: Indiana JonesRambo vs. Ripley Bear Grylls 2.0 might give Ripley a somewhat harder fight, but he still hasn't got shit against xenomorph senses and flamethrowers.
Winner: RipleyBlack Widow vs. Some gladiator dude A gladiator fights one on one, face to face, in the arena. A superspy does not.
Winner: Black WidowXena vs. Alice Xena is super badass but Alice... she stares at that guy through a camera and his eyes start bleeding, what the hell? Even though I don't like it,
Winner: AliceLara Croft vs. Leonidas Leonidas was killed by arrows, Lara Croft has bullets. Loads of them.
Winner: Lara CroftConan the Barbarian vs. Sarah Connor Aww, I wanted Conan to get further. But Sarah Connor killed Arnie when he was a murder robot, I can't believe she would have problems against him as a human.
Winner: Sarah ConnorRound 3Indiana Jones vs. Ripley "Nuke the entire site from orbit. It's the only way to be sure." Indy goes into an old fridge and survives. No but seriously, Indy will fool around for a while, but he's just a guy with a whip and Ripley is Ripley.
Winner: RipleyBlack Widow vs. Alice Does T-Virus beat enhanced physique? My guess: Yes, it will just create some new weird power for Alice and Black Widow is too well defined to compete.
Winner: Black WidowLara Croft vs. Sarah Connor Lara Croft's been fighting things from dusty old tombs. Not killer robots from the future.
Winner: Sarah ConnorRound 4 - FinalsRipley vs. Alice vs. Sarah Connor Let's see here. A woman with xenomorph powers who has spent a lot of time fighting said insanely dangerous xenomorphs. A T-Virus infectee with all the crazy powers and great combat skills. The number one killer of unkillable future robots. This is the ultimate showdown. They fight and fight and fight. And then...

Secret Faction activated:
Samuel L. Jackson (aka Ray Arnold)You thought he got eaten by raptors? Well then you were wrong! He fought those raptors like a boss but he needed something to hit them with. So he tore off his own arm, beat them up, and they ran away. Then he ran into a T-Rex. They became best pals because they were equally awesome. The T-Rex ate some raptors so the rest of the main characters could escape. But Samuel L. Jackson stayed on the island with his new buddy. And now he's had it with these motherfuckin' hunger gamers on this motherfuckin' island.
Samuel L. Jackson rides the T-Rex right into the final battle. Ripley thinks she's such hot shit but she fought an alien queen, not a TYRANNOSAURUS REX. She gets eaten. Alice tries the blood-out-of-eyes thing on Samuel L. Jackson, but he just stares right back and her head explodes. Then he turns to Sarah Connor who gets ready to fight but he says:
"Normally, your ass would be dead as fucking fried chicken, but you happen to pull this shit while I'm in a transitional period so I don't wanna kill you, I wanna help you. But I can't give you this case, it don't belong to me. Besides, I've already been through too much shit this morning over this case to hand it over to your dumb ass."
"On August 29th, 1997, it's gonna feel pretty fucking real to you too. Anybody not wearing 2 million sunblock is gonna have a real bad day. Get it?" Sarah Connor responds.
Turns out they have a common goal - the Death Star.
Sarah Connor, Samuel L. Jackson and T-Rex all go to the Death Star. They rampage through the place slaughtering everyone. Sarah Connor takes out the T-1000 of course, and Iron Man to be on the safe side. Samuel L. Jackson finds Emperor Palpatine and throws him out the window. Then he kills Boba Fett, finishing that whole thing. T-Rex eats most everyone.
The world is saved!
Remus: Harry... I'm a werewolf.
Harry: Are you fucking serious?
Remus: Well yes, but I don't see how that applies here.