The graphic novel 300 (and really, the real-life battle that it based on) makes a note of showing that all of the 300 Spartans (particularly King Leonidas) are some of the most badass determinators imaginable.
It's also important to note, in final day of the real-life battle, the Thespians (from Thermopylae not the other kind) who also stayed with the Spartans to the end to protect the allied retreat. The Thebians, on the other hand... not so much (they eventually surrendered).
The Blue Knight, who once hunted Royal Williams over several months for the crime of unloading stolen merchandise, even chasing him down while the planet was literally shaking itself apart.
In "The Tarnished Angel", Steeljack becomes one when he finally figures out what's going on. An 800-pound man made of steel is pretty darned unstoppable when he wants to be.
Krigari Ironhand. Guy just did not give up. His whole motivation was being told he'd be defeated by the Honor Guard and doing everything, including mining a broken universe, to find a way to beat them (neatly ignoring that they wouldn't have been a problem if he'd just not fought them at all).
Infidel, Arch-Enemy to Samaritan, is Astro City's hands-down winner of this trope. The man thinks nothing of waiting millennia to wear down Samaritan's heroic resolve and come around to Infidel's point of view.
Smiley Bone from Bone shows elements of this from time to time, either because he's stupid or insanely optimistic.
His ancestor Big Johnson Bone (from the prequel Stupid, Stupid Rat Tails) lives and breathes the trope.
And possibly for the same reason as Smiley; as he seems to have a severe lack of intelligence and reason. He believes, among other things, that he has been dead before and came back to life, that he lost his sanity and found it again, caught five hundred muskrats with a single raisin, and that he encountered an Ace of Spades playing card in some extremely intricate scenario that takes a whole day just to describe and somehow involves a competition, a stuffed possum, and a massive explosion. Though, his Determinator mindset is a little more justified in that he's strong enough to kill a BEAR when he was just a newborninfant.
Paulie from Circles is very determined and tries to get as much done as possible. He wants to live life to the fullest and as a result, he lived and prospered much longer than other HIV positive patients. He was suffering from aches and pains and kept quiet about it until his condition worsened. Even on his deathbed, he fought to stay alive to say his goodbyes to everyone he loves and all who loved him.
The titular Ax-CrazyHate Plague infectees in Crossed. When they set their minds to committing some sort of atrocity, nothing will deter them. In Crossed 3D, there's a recurring exchange (first seen when the protagonists watch a horde of Crossed topple a skyscraper with nothing more than torches and melee weapons) that goes like this: [character]: "How the hell did the Crossed manage to [improbable achievement]?" [other character]: "Tenacity."
This is THE essence of Donald Duck, the ultimate everyman. Life is grim, he rarely triumphs, when he does his victories tend to be hollow, no one gives him a break...and yet, he'll always keep on trying. There will be no job he won't tackle, no task he'll turn down if the thinks he can succeed at it, despite every single thing going against him.
Paperinik New Adventures. As Paperinik (his superhero persona), Donald had to face Trauma, an EvronianSuper-Soldier who has immense Super-Strength and the ability to amplify his foes fear before absorbing it and enslaving them. Knowing what he could do, he came with a Power Armor that matched Trauma's strength and protected him from the psychic powers, but then he lost the helmet, Trauma used his powers to overwhelm him with fear... And he fought on◊, scaring the hell out of Trauma and making him plea for mercy as he lost his powers! And it's not like he wasn't scared because he was a superhero (as the Evronians and Uno thought): he plainly admitted he was terrified, but he had to stop Trauma, and so he fought on.
The Evronians themselves are incredibly tenacious: the only way to make them back down is overwhelming firepower, and all you've got is a temporary reprieve before they come back with overwhelming firepower or other means to defeat you. It says everything that they still go after Xadhoom fully knowing the scale of her powers and that she has a genocidal vendetta against them: an early encounter revealed them that harnessing her power could solve their impending energy shortage, so they've determined to do just that, and came close to succeed multiple times
Surprisingly enough, Empowered is one if you think about it. Setting aside the fact that a sane person would have hung up the hypermembrane a long time ago rather than put up with the constant humiliation at the hands of almost everybody, her boyfriend once had to shred said suit in order to keep her from responding to an alert, concerning a local "Heavy Hitter" on the move, when she was so sick she could barely stand (then heanswered said summonswith nothing more than a sniper rifle). In later volumes, Emp demonstrates that suit or no suit, if she's mad enough, she is unstoppable. "This... is... what... I... AM!"
Judge Dredd. With no means of transportation left to him, he travels through Death Valley on foot to deliver a plague vaccine to a desperate Mega City Two ("The Cursed Earth"). With Mega City One left defenseless and completely open to saturation bombing and invasion, he refuses to surrender his city to East Meg One ("Apocalypse War"). With his eyes ripped out, he still blindly runs a gauntlet against a psychic mutant monstrosity that can remodel the world around him ("City of the Damned"). There's just no stopping the guy.
In Necropolis, the Dark Judges burnt his face off, threw him into an acid river and left him for dead in the radioactive wilderness. Big mistake..
Perhaps the only real power Kick-Ass possesses is the fact that he never, ever gives up. Even when he gets strapped to a chair and gets his testicles electrocuted for half an hour, his plan for getting out of it is to get the mobsters to punch him until the chair breaks. Then he gets right back up and tells them to bring it. They do, but luckily Hit Girl returns just in time to eviscerate them all. Which is either pretty solid deconstruction or straightforward badass. The fact he keeps at the whole superhero thing even when he knows full well that the world's not worth saving is supposed to be a gut-wrenching demonstration of the kind of depths of despair and nihilism he's fallen to, but it reads more like a very well written Moment of Badass.
The Mask: Walter. He never stops and appears to be the only being on the planet the mask Just. Can. Not. Kill. (and not for lack of trying, either).
Issue 81 features the story of Wind Sock, an earth pony whose lifelong dream was to become a Wonderbolt. To that end, he experimented with aeronautics, hoping to develop something that would let him fly with the pegasi. Time after time, he would build something, test it, crash, and set out to try again. He finally achieved his dream when he built a glider, used it to rescue an injured Wonderbolt, and was rewarded with a place in their ranks.
In My Little Pony Micro Series Issue #2 Rainbow's refusal to give up is specifically mentioned by a pony reporter at the end of the comic.
The to be-Saint of Killers from Preacher managed to retain his mind even in death by pure hatred of the two men who he had swore vengeance on. And then he became invincible, and unstoppable, and the world trembled at the thunder of his guns.
He's usually an idiot, but when Rat-Man gets properly motivated nothing can stop him. Early in his career, he fought Manga characters in an arena, always losing, and always coming back for new battles, even after getting a No-Holds-Barred Beatdown by Kenshiro. His last fight in the arena was against Il Drago (that's Italian for "The Dragon"), a Son GokuExpy that nobody had ever scored a hit against, let alone defeated, yet not only he did not ask for mercy when the stone Il Drago was beating him with did, he socked him on the nose. In one occasion he fought a cyborg (later revealed to be a Brainwashed and CrazyThing), and no matter how many times he got punched, he always got back up and, in the end, won. For a brief period he had been paraplegic, and somehow he managed to jump on a demonically possessed foe while still on a wheelchair. And when The Shadow made him fight his own shadow, a fight all other superheroes had failed, he won, because he just wouldn't lose his hope to meet his late love Thea again. Then tearfullySubverted when the Shadow shows him that the one world where Thea would still be alive would be the one where they never met.
Red (2003) has Paul Moses, although this is more because despite the fact that he's an old man and retired, several teams of professional killers sent after him and an entire building full of soldiers he has to fight through do not deter him in the slightest. They send wave after wave of men at him and he slaughters all of them without so much as a scratch.
Friday in Rogue Trooper, when he crosses two hundred miles in a few days to take down Highsight while being occasionally attacked by rogue grunts.
The original Rogue tracks the Traitor General across Nu Earth to avenge his comrades.
Simon Wiesenthal in Simon Says: Nazi Hunter is determined to bring down all the Nazis in the Third Reich, and he won't let anything stop him, from being told to stop because people are losing interest, to a lack of evidence to convict them.
Basically, every main character in Sin City: Hartigan, Marv, Dwight, Wallace... some of the predicaments that these characters find themselves in are flabbergasting, yet they never show more than the slightest notion of fear in their endeavors.
The very first Sin City yarn is a prime example of this trope. A Hooker with a Heart of Gold named Goldie was killed, and Marv survived multiple injuries (he had to get himself bandaged up at least twice), including gunshots, being hit by a car and being hit in the head with a sledgehammer, to avenge her death because she slept with him (and took his virginity), even though in all likelihood she was just using him for protection and felt nothing for him (though her twin sister Wendy, Marv's companion, did come to care for him). Even when he's on Death Row and they execute him at the electric chair, it takes two tries to finish him.
At one point in his Sonic the Hedgehog (Archie Comics) spin-off series, Knuckles is at the mercy of the powerful demigod Enerjak, who tries all sorts of things to break Knuckles' spirits, from teleporting him to the moon, to the bottom of the ocean, to dropping him from 30,000meters in the air, but Knuckles will not break.
So long as something existed to menace Mobius, Sonic would never give up. Best exemplified by the speech he gives to Robotnik when the latter has absorbed the power of the Chaos emeralds to attain reality warping powers, while they're fighting through a series of increasingly bizarre scenarios.
Sonic: Change reality any way you like, Robotnik! Whatever you do I'll still fight you, and somehow I'll win! Because no matter how ridiculous the situation, I'll never give up, Robotnik! I'll never give up!
In one story, Sonic fights a robot that can predict his every move and counteract it. So Sonic gives up. Since the robot was programmed to believe that this circumstance would never happen, it malfunctions and blows up, which is exactly what Sonic intended.
Zone from Special Forces, a severe autistic cajoled into the military by a desperate recruiting officer. He follows a list for his daily activities, and if it's on the list, it gets done. When his squad's first mission goes sour and only he and Felony are alive, he adamantly refuses to stay down; the mission was on the list, and he's not going to stop until it's completed or he's dead. Later, when he's captured, the enemy leader remarks that "Long have I heard tales of the indomitable will of the American fighting man... this one is something else. Superhuman! It's as if he could not feel pain!" Zone would eventually ride a motorcycle up a giant sword to jump into a helicopter carrying his quarry, and sacrifice himself at Felony's behest for the sake of the mission.
The Transformers (IDW) has pre-Matrix Orion Pax, who after learning just how corrupt the Senate is, through narrowly surviving an attempt on his life, marches all the way from his police station to the Senate Chambers, carrying their reluctant minion Whirl on his back, then ploughs through their security, later established to be a hundred-strong army of trigger-happy Triple-Changers, and immediately after taking the floor begins lecturing the Senate on how much they suck, even as some of their goons start dragging him out.
The Kraken in The Umbrella Academy. Despite having the near-useless power to breathe underwater, he's one tough mother, and probably the most formidable and successful crime-fighter on the team.
In Violine, Muller, the Greater-Scope Villain, keeps pursuing Violine and her father, even after apparently being killed by crocodiles — twice. He also expresses his determination to never give up on finding them.
Kenton of White Sand. While he points out himself that determination is no substitute for ability he lacks, he manages to climb to the highest rank of Sand Masters by sheer stubbornness, then survives being buried under a metre of sand with sheer willpower and protects his remaining people with little more than zeal.
◊, scaring the hell out of Trauma and making him plea for mercy as he lost his powers! And it's not like he wasn't scared because he was a superhero (as the Evronians and Uno thought): he plainly admitted he was terrified, but he had to stop Trauma, and so he fought on.
