It's easy enough to miss, but Shang actually sends Mulan off midway through the "I'll Make A Man Out Of You" segment. That's right, he sent her home and relieved the Fa family of their war duty. But she pulled through because of her pride and intelligence.
Nana from Madagascar and Madagascar: Escape 2 Africa is a parody of the trope.
Also in the sequel a shark so determined to take a bite at Mort that it chased him onto the shore, across the jungle and up a volcano.
Captain DuBois in Europe's Most Wanted. She even follows the animals to New York, well out of her jurisdiction.
Subverted at the end of the original, where he and Tack are fighting over the balls, and the Thief just decides that they're not worth it and walks away
Po from Kung Fu Panda stuck around with Master ShiFu despite Training from Hell that was specially designed to drive him out of the temple. And he was an unfit panda with next to no kung fu training who was undergoing stuff that kung fu masters many times his level did. Not to mention the fact that he was once kicked off the temple and had to climb up a few thousand steps to return. He Took a Level in Badass when his natural kung fu abilities were discovered.
He continues the trend in the sequel. Get shot with a cannon? Not a problem. Come back and challenge the Big Bad. Get blown up? Get back up and destroy the Big Bad's fleet.
Abbot Cellach in The Secret of Kells. He gets shot by an arrow that's on fire, stabbed through with a sword, is left for dead during a winter night, and he lived for over a decade afterwards.
Carl, from Up. A first-class grump, but when the chips are down, will not let a kid be harmed on his watch.
Monsters University reveals that Mike is one. Ever since he was little, everyone and their mother tell him that he's not a scarer, but he refuses to listen to them. Mike and Sulley also get a duo moment of determination when they work their way up from mailroom employees to scarers, step by step, after having their spirits crushed by getting kicked out of college.
Vanellope Von Schweetz from Wreck-It Ralph has the prime directive to just cross the finish line of her game Sugar Rush. She aims to do that...and win.
Anna in Frozen. She takes off after Elsa in the winter storm in a ball gown to avoid losing time, strong arms a man she doesn't know into helping her, attempts to climb a mountain with no mountaineering skills, refuses to leave her sister's castle despite being struck in the heart by ice magic, and eventually gives up her own life so that Elsa can live.
Given the hellhole of a future he lived in, Reese himself must have been one to survive. Also, Sarah embraces her inner Determinator in the climax of the first movie, and practically becomes a Terminator in the second, to the point she's halfway to shooting a defenceless, wounded man in front of his wife and children for something he hasn't actually done yet. Even after that, she's still perfectly capable of firing a 12-gauge shotgun repeatedly after minutes earlier having an inch-thick metal spike rammed straight through her shoulder. In fact, if she hadn't run out of ammo, she would have destroyed the T-1000 herself, without the T-800's help.
The cyborgs played by Arnold in the second and third films get as much damage as they can, but don't give up on the mission of protecting John Connor and only stop after the enemy's been neutralized (in the third, in quite a literal way).
In the newest Terminator film, the last lines spoken are this trope to a T.
John Connor: This battle has been won, but the war against the machines races on. Skynet's global network remains strong, but we will not quit, until all of it is destroyed.
James T. Kirk in the 2009 Star Trek movie fits this trope perfectly. He doesn't believe in no-win scenarios and is certainly one stubborn fellow once he sets his mind to accomplishing something, be it graduating from Starfleet Academy early, finding a way to beat the supposedly unbeatable Kobayashi Maru, or stopping Nero. He takes more beat-downs than any other character and is consistently degraded or doubted by those around him, but keeps coming back for more in order to protect his homeworld. He is certainly not too worried about getting himself killed in the process, either.
Kirk pretty much sums up his no-win scenario beliefs by saying, in regards to the Kobayashi Maru and many of his persistent actions, "It depends on how you define 'winning', doesn't it?"
He does the same thing in the sequel. Also, arguably, so is Spock, right after Kirk performs a HeroicSacrifice to save the crew. Spock decides to take revenge on Determinator Khan, beaming down to Earth and chasing after him with the sole purpose of killing him. It's only after Uhura reveals that Khan's their only chance to bring Kirk back to life that he stops.
Paul Rusesabagina, whose Real Life story was chronicled in Hotel Rwanda, which is often referred to as an African Schindler's List. During the mass genocide in Rwanda in 1994, he managed to save nearly a thousand people who had been marked for death by sheltering them in his hotel and transporting them to safety, and standing up to corrupt military officials and screaming, machete-wielding mobs, all without raising a single firearm.
Paul: There will be no rescue, no intervention for us. We can only save ourselves.
Paul Newman's character Luke in the movie Cool Hand Luke is a perfect example of a Determinator. Acts of sheer determination include eating fifty eggs in under an hour to win a bet, multiple attempts to escape from jail, resisting the worst the warden could give him, and "winning" a boxing match by repeatedly getting up, no matter how many times he was knocked down, until his opponent, who was so far unharmed, refused to hit him any more. His nickname came from his habit of keeping going and refusing to quit when he has absolutely nothing - specifically, the time he won a poker game by bluffing.
Dragline: Nothin'. A handful of nothin'. You stupid mullet head. He beat you with nothin'. Just like today when he kept comin' back at me — with nothin'. Luke: Yeah well, sometimes nothing can be a real cool hand.
Both Neo and Agent Smith of The Matrix are up there - Smith possibly even more so. During their final battle, Smith's inability to understand Neo's refusal to stay down drives him out of his mind.
John Creasy from Man on Fire. Being severely wounded with a partially collapsed lung does not deter him from hunting down, torturing and killing the kidnappers of his charge or anyone else involved.
Ethan Edwards, the Confederate soldier-turned-Indian hunter in The Searchers.
Ethan: Injun will chase a thing till he thinks he's chased it enough. Then he quits. Same way when he runs. Seems like he never learns there's such a thing as a critter who'll just keep comin' on. So we'll find 'em in the end, I promise you. We'll find 'em, just as sure as the turnin' of the earth.
Jason Bourne. At various times, he's shot, thrown off buildings, beat to a bloody pulp, put through horrendous car crashes, been right next to an exploding bomb. And he just gets up, hunts down who did that to him, and keeps on trucking.
The crew of the Leper Colony in Dr. Strangelove will complete its mission, no matter what.
Porter from Payback wants the money he is owed, will not be stopped by anyone.
Harold Abrahams in Chariots of Fire: "I'll take them all on, one by one, and run them off their feet."
Will 'Elizabeth goes free!' Turner in the first Pirates of the Caribbean movie. He has a one track mind about saving her, and he's certainly not too worried about getting himself killed in the process, to the point that he was one of the inspirations for the Martyr Without a Cause trope.
The protagonist of the 2007 remake of 3:10 to Yuma certainly doesn't Know When to Fold 'Em, and it's not even about the money. No one (maybe even not he himself) knows why he's so determined to keep going until the end, though one reason is to make his son proud of him. He wins everyone over by sheer amazement about his stubborn determination. Not that that's enough to save the day, but pretty close.
And Norman, in the battle. Right after getting killed as an Avatar, which was almost fully Your Mind Makes It Real, he picked up a machine gun and charged back to the battle in his puny human body.
The protagonist from Taken. Nothing will stop him from saving his daughter. NOTHING.
Bryan: I will look for you, I will find you, and I will kill you.
Smokey and the Bandit's Sheriff Beuford T. Justice. Run him off the road, plow through his car with an 18-wheeler, run him through a minefield which reduces his police cruiser to nothing but a chassis, engine, and steering wheel. Nothing will stop him from chasing The Bandit.
Crank: Chev Chelios takes this trope to its logical extreme: if he stops, he literally will die.
Patch Adams has a weird vibe on this. Adams is "determined" not to do simple things like obey the rules in a hospital or dress up in clothes for his graduation ceremony because he believes that giving people joy override everything else. It's ironic because he doesn't understand that basic people skills like not alienating your professor to the point where he wants to expel you, will also allow you to go far with your goals.
Rudy was about a guy who never gave up and that was his redeeming quality. The real-life story is also interesting. He was so determined to make a movie about his life, that the coach agreed to let himself be portrayed as a villain so that the movie would be greenlit.
This is the basis of the Clousseau's success in The Pink Panther according to David Niven's character. He said in an interview in the last sequel to The Pink Panther that Clousseau was a bumbling idiot but he succeeded because he obeyed "The 11th Commandment. Never Give Up." This doesn't really make sense, since Clousseau succeeded because the writers needed him to succeed, because he was the hero. But it's a nice afterthought.
Sands (Johnny Depp) in Once upon a Time in Mexico. Halfway through the film, the villains start to catch on and decide to drill his eyes out. It doesn't stop him. AT ALL.
Apollo 13. Pretty much everyone in NASA will not give up until the astronauts make it home. Gene Kranz in particular. "Failure is NOT an option."
Many examples from Lord of the Rings, but particularly Sam. He wades into a river chasing Frodo even though he can't swim, resists the lure of the Ring, and literally carries Frodo through the last leg of the journey even though both are near death from exhaustion.
Garcia from the SyFy movie Yeti. Survives a plane crash, travels out into the wild to find the spare radio in the other end of the plane. Breaks his legs running from a yeti, splints the leg with the severed arm of his body, gets chased all the way back to the plane, dragging the radio with him, shot in the eye with a Flare Gun when the jerkass of the movie panics and thinks he's the yeti, and wakes up at the end of the movie to see one of the yetis' arms popping out of the snow. And the movie started with his coach telling him that he "needed to show more heart"
Watanabe from Ikiru keeps on pestering the bureaucracy till they give in and build a park over the mosquito-infested cesspool.
The title character of The Book of Eli takes his 'mission' seriously enough to continue walking after he's been shot in the gut.
Vincent "Jerome" Freeman in Gattaca; judged to have a life expectancy under 31 years and subject to debilitating heart weakness, he nevertheless becomes an astronaut despite everyone, from his mother to the original owner of his donor identity, telling him it's impossible. Also, he gets to come home to Uma Thurman.
The Princess Bride: Hello. My name is Inigo Montoya. You killed my father. Prepare to die.
Angus from the movie Black Sheep. After being turned into a sheep monster, he gets into a Helicopter Blender, GETS BACK UP, gets turned back into a human and is shown to be missing most of his skull, GETS BACK UP, and wanders into the horde of monster sheep to... rejoin the flock. It ends poorly for him.
Ace Rothstein's initial description of Nicky Santoro in Casino highlights exactly why you should NEVER pick a fight with him:
Detective Murakami in Stray Dog. After his gun is stolen, he does not stop looking for it. And each time he finds out it's used in a new crime, he only becomes more determined.
127 Hours: Aron Ralston (also under Real Life examples). His arm is crushed under a boulder while he's hiking, trapping him in a crevice with only the food and water he'd brought for a one day hike. Just surviving as long as he does (five days!) is a feat unto itself, even if he hadn't amputated his own arm with a dull multitool, rappelled down a cliff, and walked for eight miles before he found rescue.
Hoffman in Saw 3D. He wants Jill. He isn't going to let anything, like a police station full of cops, get in his way.
Unstoppable: Frank, in pursuit of 777. Lampshaded somewhat when he tells Will that he gives up too easily.
Godzilla: He is a prime example of a Determinator, fighting to the death even when its clear he's gonna lose and has a tendency to solve any problem he's faced with with Brute force or cunning. Flying Enemy? No problem, use atomic breathe to propel you. World destroyer in your base killing ur dudez? Gather up the posse and take it down.
Winter's Bone: Nothing will stop Ree from saving the family home. Nothing.
True Grit's Mattie Ross. A 14-year-old girl in pigtails, alone in the American West, is nobody's idea of an arbiter of justice. Nonetheless, she's bent on catching her daddy's killer, and no concerned mother, nor Texas Ranger, nor eyepatch-wearing bounty-hunter, nor wide river, nor bitter weather, nor cold trail, nor misfiring gun, nor band of outlaws, nor 100-foot-deep pit filled with snakes is going to keep Tom Chaney safe from retribution..
Michael Myers from the Halloween series spent fifteen years in a mental hospital, waiting for a chance to escape so that he could kill his sister. When he failed in killing her, he then spent the next ten years massacring everybody related to her. Then, depending on which canon you follow, he spent 10-20 years searching for his sister again.
Dr. Samuel Loomis as well. He refused to allow anything to keep him from stopping Myers'.
Firefly's Malcolm Reynolds proves himself to be The Determinator over and over again in his Big Damn Movie. At one point in Serenity he takes a sword to the gut and keeps on fighting. That's determination. His antics can also be found on the Live Action TV page.
The Lord of the Rings: Samwise Gamgee. Is Frodo's only companion to stay with him clear from the Shire to Mt Doom, in spite of being turned away by Frodo twice, and in spite of Frodo and the others twice secretly conspiring with regards to the journey without Sam or the other hobbits. He also saves Frodo from an Eldritch Abomination and Orcs, then carries him partway up Mt Doom on his own back. The only incentive he gets to do any of this is when Gandalf says, "Don't you leave him Samwise Gamgee" once, right at the beginning.
The final assassin (Yan Xiaogou) is a highly-skilled martial artist, and as such, he is unstoppable in close quarters against the mostly untrained opponents he fights. After mowing down a lot of bodyguards and a major named character, one of the last few survivors shoots him. Reality Ensues.
Winner for the film, though, must go to Liu Yubei. He's introduced as an unkempt tortured drunkard beggar, then appears in bishonen form as The Cavalry to the convoy, with a Grand Staircase Entrance. He then holds his choke point on the stairs alone against dozens of trained assassins who, to this point, have barely met an even match in single combat. The assassins resort to using chains and hooks, slowly wearing him down to the point where he could barely stand, yet Yubei kills or incapacitates every single one aside from Yan Xiaogou. And still goads Xiaogou into delaying long enough to cut him down thoroughly by cutting off the tail of his queue.
DA Frank Scanlon in The Green Hornet is a comical example. when he is revealed to be the main bad guy, he chased the Duo from one part of the city to the other, went all the way to the top of the Daily Sentinel news building. By the time he caught up with the duo he was so out of breath that he couldn't even remember what the name of the flash drive was that had evidence against him.
Scanlon: Alright Reid, hand over the thing.
Vincent in Collateral. After getting in a 100 mph car crash without a seatbelt, he just gets up and runs away. A few minutes later, he gets shot in the face...and just walks it off.
Matsu in the Female Prisoner Scorpion series. Lock her up, tie her up, beat her: she just waits for a chance, manipulates the people around her, and escapes to pursue her grudge. Thrown in a freezing, dark underground cell for a year, hands and feet shackled, what does she do? Carve a spoon into a shiv - in her teeth.
Steve Rogers, aka Captain America, in Captain America: The First Avenger. Much like his comics counterpart, the man does not know the meaning of the word "quit", whether he's being beat down by regular bullies or superhuman Nazi despots.
"I could do this all day."
Even when Steve's undergoing the Super Soldier transformation procedure, we have the staff telling Dr. Erskine to stop the experimentation, in fear of Steve potentially dying. However, Steve won't have any of that, actually yelling for the Doctor to keep going with it.
"NOOOOOO! Don't! I CAN DO THIS!"
Bud Fox, from Wall Street, is definitely persistent in trying to work his way up the stockbrokers' world.
In The Guardian we meet a guy named Hodge who has washed out from the Coast Guard rescue swimmer school twice and is back for a third go.
All the Ghostfaces in Scream. They are beaten by anything the stalked victims have at hand (including doors), trip, fall down stairs... and still keep on going after the victim. (And only Plot Armor saves you)
In the 2011 film Warrior: This is Brendan's primary fighting style, highlighting him as the hero of the film. He's a heavy underdog all the way through, but always manages to persevere and find a way to win via sustained grappling. In the end, Tommy also shows himself to be, but in a more tragic way. He keeps fighting even after his defeat is certain, refusing to just let go because he's determined to support his best friend's widow and he breaks down when he realizes that he can't win with one arm. This sets Tommy apart from Koba, who taps out when in the same position.
Dr. Elsa Schneider in "Indiana Jones and the Last Crusade" was determined to get the Holy Grail at any price, including working with the Nazis and sleeping with Indy AND his father. At the end of the film, she attempts to steal it and triggers a Cataclysm Climax when she steps over a protective seal. She crashes to the ground and watches the grail rolls away from her, and despite the structure collapsing all around her, she dives after it, which causes her to nearly fall into a crevasse. Indiana, however, catches Elsa just in time, only to have her use her grip on his hand as leverage to reach for the grail below her. Before long, her hand slides out from its black glove and she falls to her death: her determination (see: obsession) serving as her undoing.
Jeepers Creepers: The Creeper. Kills anyone that gets in his way, will lose most of his limbs, get harpooned in the head, get's stabbed multiple times, has to grow a new HEAD and is overall gonna stop at nothing to catch his prey!!!
From 42, nothing is going to stop Dodgers manager Branch Rickey from getting an African-American player into Major League Baseball. If you're an employee or player who objects to having Jackie on the team, he'll fire you without a second thought. If you're an opposing team who refuses to play against Robinson, he'll damn your eternal soul.
Very much Zod. Even after the entire destruction of his ship, crew, terraformer, and everything he was going to use to turn Earth into Krypton 2.0 was destroyed, he still tried to do "what is best" for Krypton. He also overcomes the debilitating effect of his new haywire Super Senses by concentrating really hard.
Raleigh from Pacific Rim. He's able to handle his mech's neural load solo (it normally takes two people) long enough to kill the Kaiju attacking his mech after it had killed his brother (while they were still connected) and walk it to shore without guidance from mission control.
Stacker Pentecost even more so, as he pilots Coyote Tango solo versus Onibaba after his copilot blacks out from cancer-induced stress for THREE HOURS.
In The Heat both Ashburn and Mullins go far, even past physical pain, to catch their perps.
Max, as he's trying to save his life from imminent death. Nothing gets in his way from reaching Elysium , not lethal irradiation, not painful Exo-Suit surgery, not even a stab wound keeps him down for more than a day or so.
And Kruger. It's his job to be one, though. But his hunt for Max quickly becomes personal, especially when Max blows half of Kruger's head right off
Scientist Jane Foster in Thor. It's clear from her very first scene that she's ready to do anything for her research, namely driving directly into a tornado to get the data necessary to prove her theories.
Scout Leader Erikson in Bushwhacked gets his hands cuffed around a tree, but gets out of it by climbing. Using primarily his feet. And breaking off the branches in his way.
Even 15 years after the Janjira incident, Joe Brody hadn't given up on finding the truth.
Godzilla chases the Muto relentlessly for miles and when he finally catches up to them, continues fighting even as he was being mauled by the two at once while constantly getting back up no matter how severely he's beaten down. Even a skyscraper collapsing on him only slowed him down for a few minutes.
Angry mama MUTO after realizing Ford destroyed her eggs.
The Driver in Shuttle is a villainous version. Car crashes, tire irons to the skull, stab wounds, a bullet to the face... it won't stop him from getting his product out.
Kitty, who must keep the link open, is at one point stabbed by Logan when his present body reacts violently to mental trauma in the past. And due to how time runs concurrently in the past and present, it's implied that it takes a few days before Logan and co. can properly stop Mystique, which means that she is slowly bleeding out and can't sleep for that period.
Same goes for Mystique, who throughout the film finds more and more damning evidence that Trask really needs to be killed. It's not until the very end that Charles manages to talk her out of it.
The Prototype Sentinel that goes after Magneto definitely is this. Even as it's being torn to pieces, it still tries to grab him.