Manolo Sanchez from The Book of Life. Not even death can keep him away from Maria.
Héctor from Coco, who has spent 96 years of his afterlife trying to cross the Marigold Bridge on Dia de Muertos to be able to see his beloved daughter Coco.
Anna in Frozen. She takes off after Elsa in the winter storm in a ball gown to avoid losing time, convinces a misanthropic stranger 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, finding the willpower to sprint to put herself between Elsa and an incoming sword despite having almost completely frozen from the inside out.
In Home, nothing will stop Tip from getting to her alien-abducted mother. That includes the distance between continents and a total lack of knowledge as to where she was even taken. She does briefly lose hope when she's found the other humans but has no idea where to look, but Oh comes back just in time.
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. This what earned him the respect of most of the Furious Five, and he Took a Level in Badass when his natural kung fu abilities were discovered.
Po continues the trend in Kung Fu Panda 2. 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.
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.
Pixar must be fond of these characters. Going down the list, we have:
Woody. In all three Toy Story movies. He never really gave up on Andy, even when he gave up on himself and even when the other toys gave up on either him or Andy. Or both. Andy sums this up at the end of Toy Story 3:
Andy: But the thing that makes Woody special is he'll never give up on you. Ever. He'll be there for you, no matter what.
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.
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.
Spirit: Stallion of the Cimarron: Spirit. As in, the horse. There are scenes in which it looks like his spirit's been broken, only for him to fight back again with renewed vigor.
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.
Judy Hopps of Zootopia. Fighting a bully who's twice her size? Training to become a cop despite everyone telling her it's impossible? Taking on a case even though she has only 48 hours and no resources? Whatever the goal, once Judy decides to take action, nothing can stand in her way. She means it when she says she doesn't know when to quit.
Film - Live Action
The protagonist of 3:10 to Yuma (2007) 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.
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.
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.
Lance Corporal William Schofield from 1917. Determined doesn't even begin to cover it.
General Erinmore: Down to Gehenna or up to the throne; he travels the fastest who travels alone.
Angus from the movie Black Sheep (2007). 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.
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.
The title character of The Book of Eli takes his 'mission' seriously enough to continue walking after he's been shot in the gut.
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.
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.
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 can 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!"
It gets one step further when dealing with Thanos, one of universe's strongest beings - in Avengers: Infinity War, he grabs Thanos by the hand to shortly hold him back; and in Avengers: Endgame, where he actually manages to give Thanos a fight, once the struggle leaves him wounded, disarmed, with his previously indestructible shield in pieces, and facing down not only Thanos but an army of hundreds, Steve just straps the remains of his shield tighter to his arm and get ready to take them all on.
I keep telling people to move on. Some do. But not us. Not us...
If none of his post-procedure feats do anything for you, having this veritable laundry list of ailments during The Great Depression, a time when employment was hardly guaranteed and most of these conditions had no effective or affordable cure yet, certainly will. Steve, the shrimpy dork from Brooklyn, had to be a supreme Determinator just to live long enough to be Captain America.
Captain Marvel never gives up, no matter how the odds are stacked against her. At one point we see flashbacks of her being repeatedly knocked to the ground, but each time she falls over, she gets back up again. It's this determination that allows her to activate God Mode at the climax of the film.
Kelly Sue DeConnick: Carol falls down all the time, but she always gets back up — we say that about Captain America as well, but Captain America gets back up because "it's the right thing to do." Carol gets back up because "Fuck you."
Ace Rothstein's initial description of Nicky Santoro in Casino highlights exactly why you should NEVER pick a fight with him:
Harold Abrahams in Chariots of Fire: "I'll take them all on, one by one, and run them off their feet."
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.
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.
Crank: Chev Chelios takes this trope to its logical extreme: if he stops, he literally will die.
In Cry Blood, Apache, when Vittorio finds his tribe has been slaughtered, nothing will stop him tracking down the men responsible and killing them.
Ducard: The training is nothing! The will is everything! The will to act.
Die Hard: And who could forget John McClane? The dude is a Trope Codifier for the non-invincible action hero. He's faced lethal criminals head-on while armed with only guns and an Indy Ploy and never ever stops until he gets the job done. However, he's also a Deconstruction of this trope. His determination to do the right thing always gets him battered and wounded by the end of every movie, and his devotion to seeing justice done has estranged him from his family members (to the point where he didn't even know that his own son had become a government agent).
The crew of the Leper Colony in Dr. Strangelove will complete its mission, no matter what.
Eddie the Eagle: The titular character and real life Olympic athlete is one. Nothing stopped him from achieving his dream, not the rules, not the injuries, and not his lack of skill at the sport.
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
Everest (2015): After being forced to turn back from the summit in his previous attempt, Doug Hansen is resolved to make it to the summit of Everest this time. He does make it to the summit, but this ultimately costs him his life when he becomes too ill to descend.
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.
Richard Kimble in The Fugitive. Lampshaded a couple of times.
Dr. Nichols: You never give up, Richard, do you? You NEVER GIVE UP!!!
Deputy Gerard has shades of this too, which makes them excellent foils.
Gerard: That's my man!
Rosetti: Not any more he's not. He's going down. You can help by staying out.
Gerard: ...Arrest us. (proceeds to take the building)
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.
Maximus Decimus Meridius from Gladiator. Nothing will stop him from avenging his family and overthrowing the usurper Emperor Commodus. Not one-sided battles, not men or tigers, not even as it turns being stabbed before what is intended to be a fancy execution — he still hands Commodus his ass.
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.
A prime example would be the comic, Godzilla in Hell; Godzilla gets trapped in Hell and has to find his way out. Facing him are the legions of Hell, eternal damnation, and increasing impossible challenges as he travels deeper and deeper into the circles of Hell. But as Hell and its denizens soon find, nothing will stop Godzilla from his goal.
Rodan is a fellow example. Up until his Monster Verse incarnation, whether Rodan was strong enough to shrug off Godzilla, or jobbing for someone else, he absolutely would not back down or submit.
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.
Another Kaiju example has to be Gamera. The amount of punishment he takes in basically all of his movies is legitimately insane, and yet his sheer willpower to keep fighting is even more so. Impaling, losing copious amounts of blood, burning, slicing, blunt force, and even getting his entire arm below his elbow blown clean off (By his own fireball, mind you, and intentionally at that.) He just powers through all of that refuses to give up, regardless of the odds stacked against him.
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.
In Grim Prairie Tales, Colochez gets shot through the throat during a Showdown at High Noon. Despite this, he manages to stagger the length of the dusty street, knock Martin to the ground, half choke him to death, and then start trying to gouge his eyes out. It is only the fact that he dies from blood loss before he succeeds that stops him from being the Implacable Man.
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'.
In The Heat both Ashburn and Mullins go far, even past physical pain, to catch their perps.
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.
Watanabe from Ikiru keeps on pestering the bureaucracy till they give in and build a park over the mosquito-infested cesspool.
Incendies: Nawal is sent to a Hellhole Prison, where she gains the moniker "The Woman Who Sings" because she defies her guards by singing in her cell. Even after being brutalized by them over 13 years, she never breaks, and she becomes something of a local legend.
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.
Karl Bélanger: Tell me we're not going to ask him to fight this election on crutches!
Anne McGrath: Try and stop him.
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!!!
The first part of Julia X is largely a battle between two determinators: with Julia determined to escape, and The Stranger equally determined to stop her.
In Jungle, Yossi is stranded in one of the most hostile environments on Earth, weeks away from the nearest civilization, and with almost nothing in the way of resources. He determines to walk his way out. And succeeds.
Last Of The Dogmen: Lewis is determined to find out the story behind the missing fugitives despite having no real incentive to do so, going to great efforts to recruit Lilian and then search the mountains. The narrator describes him as "just no good at giving up."
In Left for Dead, Clem has been following the trail of her runaway husband Blake for months. In that time she endured beatings that left her hospitalized and permanently scarred; given birth; and lost the baby. She continues to pursue him into the remotest parts of Mexico, now carrying the body of her dead son with her.
Samwise Gamgee. He 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.
Sam: I can't carry it for you... But I can carry you! (cue Reprise of Awesome of the Fellowship leitmotif)
Also Gollum, who made pretty much the same journey but under arguably worse conditions. Gollum survived starvation, torture, a trek through the dead marshes and falling off a cliff to get to his Precious. On another note, possession of the Ring extends the bearer's lifespan indefinitely but age catches up to them very quickly once they lose it. Bilbo lived 111 years while barely seeming to age until he gave up the Ring. In comparison, Gollum has staved off 600 years worth of aging and death for several years since losing the Ring. It is possible desire for the Precious is all that keeps him going at this point.
On a meta level, Mad Max was made for $400K. The director donated his own car to get smashed up in a chase scene.
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.
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.
Richie from Mars Attacks!. Not wind, not rain and certainly not an invasion with a few million hostile aliens from Mars is gonna stop that boy from getting to the retirement home to save his grandma. Extra points for being pretty much like Luigi from Luigi's Mansion: he is scared, has no real way to defend himself, but while the attacks sometimes slow him down, he never, ever stops on his way.
This is pretty much the sole reason The Martian lasts more than ten minutes. When Watney is left behind and wakes up impaled on a piece of the main transmitter, he slogs his way back to the hab, performs emergency surgery on himself, and only then breaks concentration enough to swear. While he does occasionally come close to giving up, he invariably grits his teeth and keeps going, flatly refusing to die on Mars without first doing everything in his power not to.
Also shows up in the the book constantly, to the point that when the airlock explodes, one of his audio log entries has him losing his cool and saying that he's just going to sit down and die because he's sick of all the survival nonsense. His next audio log lampshades that he's had his temper tantrum and he gets to work on how to survive again.
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.
"Why, Mister Anderson, why, WHY DO YOU PERSIST?" "Because I choose to."
Somewhat a theme of Mortal Engines, as Anna can go to great lengths due to her being The Unfettered and fearing nothing, Hester's initial determination to kill Valentine leads to six months of planning and deliberately getting herself aboard a town eaten by London just so she can have a shot at him, while Thaddeus directly compares Hester's determination to his own - he takes a serious stab wound to the gut and is back at work on MEDUSA later that day.
A Most Violent Year: Abel is an aggressive, serious-minded businessman who's determined to close on the oil terminal deal and to succeed as the better-quality option relative to his crooked competitors. Faced with the indifference of law enforcement, he ends up hunting down hijackers himself and eventually delivering an ice-cold ultimatum to those responsible.
In The Mountie, Corporal Grayling may be seen as a colossal screw-up in the eyes of his fellow Mounties, but he nevertheless shares this with them.
Cleora (narrating): In the book of the Mounties, the word "failure" doesn't exists.
In Mustang, Lale is determined to leave her grandmother's house and go to Istanbul.
Now You See It...: Allison does not take "no" for an answer, whether it's trying to convince Danny to work with her, or in trying to save Danny's life. She's always giving it her best, taking any risk necessary to complete her goal.
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.
Only the Brave: After hiring Brendan, Eric take the crew on a little jog up to a ridge and back. Brendan is tired to the point of being sick, but he completes the run shows up back at the station with a picture to prove it. Eric lets him stay on though he has to put up with taunts and jeers from the others for some time after that.
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.
Captain Vidal in Pan's Labyrinth. This makes him an utterly terrifying villain. (In fact, when he got shot in the head, he actually had the time to feel it!)
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.
Porter from Payback wants the money he is owed, will not be stopped by anyone.
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.
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.
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.
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)
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.
See You Yesterday: Claudette considering catastrophic failure after failure won't give up until her brother is saved without anyone else dying. Though the final outcome isn't shown.
Billy Batson from SHAZAM! (2019) devoted his entire life searching for his long-long mother whom he got separated from at a local fair when he was 4-years-old. He constantly broke the law and ditched his foster families in order to see her again for the past ten years. However, he was completely heartbroken upon realizing his mother never wanted him in her life.
Stantin goes more than twelve straight hours without sleep tracking down leads on the Big Bad, insists on pursuing him through a wilderness (guided by a Mountain Man) despite being a City Mouse, and presses on despite being fatigued and half-frozen. When they reach a mountain, he follows Jonathan up despite not knowing how to climb and refuses to let Knox help him out of a deadly situation until Knox promises to use a climbing rope to hoist him up the mountain rather than lowering him back down. He's also willing to go to Cowboy Cop lengths by posing as a hitman to make the villains' accomplice talk.
Knox is pretty relentless in chasing down a dangerous killer to rescue Sarah, and repeatedly tries to get Stantin to turn back so he won't be slowed down.
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.
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.
In So Dear to My Heart, Jeremiah, inspired by a song about "Stick-to-it-ivity", tries to earn money for him and his family to travel by train to the county fair by chasing a bee through a swamp in hopes of finding wild honey to sell to the general store. Despite several wrong turns and setbacks, his perseverance pays off when he finds the honey tree and earns a lot of money with all the honey he found.
James T. Kirk in the Star Trek (2009) 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 Heroic Sacrifice 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.
Let's not forget the original Captain Kirk. From Star Trek II: The Wrath of Khan to Star Trek VI: The Undiscovered Country, Kirk does what must be done, no matter what. It is from this Kirk we get the line "I don't believe in a no-win scenario." In the very next film, he asks Starfleet for permission to go back to Planet Genesis to retrieve Spock's body, and when they tell him "no" he steals his old command to do it anyway. And mind, this was just him believing he was returning Spock's corpse to Vulcan. He had no idea his friend was restored, yet. And then, on his way home to face the charges against him for this action, he learns that an alien probe attempting to contact the extinct species Humpbacked Whales is destroying the Earth. His response? He goes back in time to retrieve a pair of whales to communicate with the probe. Then submits himself for court-martial. Of course, Starfleet is so impressed with all of this that they give him back the Enterprise. Whereupon, sent on a rescue mission, he proceeds to tell a "godlike being" to go screw itself when it tries to hijack his ship. And then, just to top off an illustrious career, he helps bring about a lasting peace with the Klingons...after being framed for the murder of their chancellor by parties on both sides. And that's not counting the stuff he did in his early days back in Star Trek: The Original Series.
Rey's belief that her family will come back for her someday is enough hope to convince her to make a sparse living scavenging incredibly dangerous junked spaceships for parts (she's introduced perched diagonally on part of a crashed Star Destroyer with nothing to stop her from falling hundreds of feet to the ground), then fighting off multiple enemies to protect her valuables before selling them to the hostile junkyard manager. And she's been doing this since she was five.
Even after being shot by Chewbacca, which up until then was invariably a one-hit killer, Kylo Ren walks out to track down Finn and Rey in the snow on Starkiller Base. He then gets into a lightsaber duel with Finn and puts him a coma, then switches to dueling Rey instead, and only stops when he can no longer physically stand up—and he's still trying to get back on his feet.
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.
Suffragette: Most suffragettes. Emmeline Pankhurst is on the run from the police, but still gives speeches at secret locations. Maud is imprisoned twice, the second time she goes on hunger strike to enforce treatment as political prisoner (which the suffragettes don't get). When Maud's husband throws her out on the streets she rents an apartment with the help of the suffrage movement and continues to participate in the protests. When she loses her job, fellow suffragettes give her blankets and everything else she needs to sleep in a nearby church ... at this point, continuing the fight is the most sensible choice, as she has nothing to lose, but many would have given up regardless. Maud ... does not. There's also Edith, whose husband is worried that, with her already damaged health, another instance of Police Brutality might kill her, but Edith refuses to stay home. This is even more impressive as there's no pressure from the leaders; Emmeline Pankhurst expresses understanding for women's difficult situations and the risks they take by participating in the movement, and Edith, the leader of the local group, at one time says that everyone who doesn't want to take extreme risks can leave and she'll think no worse of them for it. Maud decides to stay.
There's also Emily Davison, who attempts to attach the suffrage movement's flag to the king's horse in a horse race, and is trampled to death. Her last words imply she was very aware of that risk or might even have intended a Heroic Sacrifice.
Bryan Mills 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.
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 Terminator 2: Judgment Day, 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. Even more so in Terminator: The Sarah Connor Chronicles.
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.
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.
It's hardly a surprise when Begbie is arrested at the end of Trainspotting. At the start of T2 Trainspotting he's been sitting in prison for 20 years, nursing a grudge against Renton. He's quite willing to go back inside if that's the price of revenge.
Alice, originating from Transformers: Revenge of the Fallen when it comes to completing her mission. In Barber's "Convergence" she murders an entire station of people while looking for the Allspark, and it's implied that this may not be the first time she's done something like this. She also gets hit by a car and reduced to pieces in the movie, only to be revealed to be very much still be ticking in the IDW comics. It takes a blade through the chest by Sideswipe after she tried to ram a NEST blockade with a vehicle containing human hostages, to finally take her out of commission.
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..
Unstoppable: Frank, in pursuit of 777. Lampshaded somewhat when he tells Will that he gives up too easily.
Valdez is Coming: Valdez is determined to get Tanner to pay $100 to the dead man's widow, and nothing-not even being beaten and left for dead in the desert — will prevent him from achieving this.
Bud Fox, from Wall Street, is definitely persistent in trying to work his way up the stockbrokers' world.
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.
Whiplash: Andrew and Fletcher each fulfill this to some extent. Andrew, in his attempts to fully access his potential as a drummer (to the point that he regularly bloodies his hands from wearing on them so often during practice); Fletcher, in how driven he is to motivate his students to succeed, even keeping Andrew and 2 fellow students isolated from the rest of the band for hours so that they can match his tempo in a harsh bit of practice.
Winter's Bone: Nothing will stop Ree from saving the family home. Nothing.
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.
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"