Tifa Lockheart in the fan film series Dead Fantasy is an insanely awesome representation of this trope. Throughout five shorts, she has been slapped with an axe capable of downing a skyscraper, beaten to a bleeding pulp, which involved literally having the Materia knocked out of her, jumped onto a train, been slashed quite a few times, filled with arrows like it was target practice, stabbed through the arm, and chained up by kusarigama. It takes Hayate's intervention to finally stop her.
In another of Montyoum's creations, RWBY, Jaune of all people. In a late episode, an Ursa, one that's bigger, stronger and more heavily-armoured than any previously encountered swats down Cardinwith little effort, so Jaune steps in to try and take it down. Even though he's physically outmatched by the creature and his Aura is low, he continually throws himself at the creature and eventually slays it. He also demonstrated this willingness to throw himself into impossible odds in his hopeless duel against Cardin earlier on.
In a Meta sense, see the page picture up there? It went through the third biggest Image Pickin Forum with the crowner with the most number of images EVER. It was open for months (IIRC) without any examples with above zero points. But guess what, we made it, and there's the picture. The people who participated in the forum are all Determinators.
The New Avengers as a whole, and several other characters as well, in Marvels RPG.
The Nostalgia Chick lives in either LA or New York City. She will run from either of these places to Virginia and Chicago to stalk and fight (and chloroform), respectively.
In The Salvation War, the First-Death humans (those who have died and are now in hell) that become main characters are basically this. Extra points because they mostly are members of the US Army. As one of its characters puts it:
Liutenant Jade "Broomstick" Kim: Okay, guys. We donít have to eat. We donít have to sleep. We heal ten times faster than ordinary humans. Weíre the United States military. Letís go blow up some baldricks.
Fantendo's user Cloverfield Monster. Despite being lynched and told to leave, he never gives up on making games.
Zerosaga1 is known for having this attribute, even when playing extremely difficult games.
Church of Red vs. Blue is basically this. He acts like he doesn't care and isn't very good at being The Hero, but if there's something he thinks has to be done, he never gives up until he accomplishes it. This goes as far as to him facing Wash and the Meta at the same time, after being shot, with just a pistol and Doc to help, after Tex is trapped in the memory unit in season 8. It doesn't work, but he still tried.
"A Simple Walk (Into Mordor)", a set of videos featuring Chris and Kerry of Rooster Teeth setting out to walk the distance between (the shooting locations of) Hobbiton to Mordor. Despite the conditions they walked across, the blisters they busted, how incredibly poor their hygiene was and how many laws they had to break to get there, they did it in six days and buried the One Ring in the site of Mordor.
Worm has several, including the protagonist, but a few stand out even among these:
Chevalier, who at one point takes a laser to to gut, wakes up an hour later having had major battlefield surgery to stitch him back up, and promptly grabs his sword and armor before heading out to challenge Behemoth, one of the deadliest entities in existence, to a swordfight.
Taylor, who in spite of being cut in half first controls her landing so as to merely break her remaining limbs hitting the water, then invoke an Emergency Transformation device to return to the fight, and then continue fighting even as (late in the battle) the transformation is wearing off and her core organs are falling out of her abdominal cavity.
I give up on giving up. I am a gamer. I CANNOT walk away from this stupid ass boss. BUG OR NO BUG. I will win.
He then works out how to do it by changing resolutions during the fight.
The Mob of Twitch Plays Pokťmon do not stop until they have defeated the Champion. No matter how many Pokemon are released, no matter how many times they lose, and no matter how powerful the enemies in front of them become, they just won't stop. As a side-effect, their hosts come across as this in-universe - Red spent days in Team Rocket HQ, AJ spent three and a half hours to get out of the first route in the game, and Napoleon spent eight hours in the Great Marsh trying to avoid disaster. Camilla A Slash gets the prize, however, for fighting the Elite Four over one hundred times.