Ga'ri in the early parts of Big Sister, still trying to recover from the Gadget Drone incident mentioned in StrikerS carries a baby across a volcanic Death World with what little power she has left, crippling herself again in the process, then manages to fight off a lethal infection and regain use of both her legs and her magic, this time without the help of high-Magitek rehabilitation facilities.
Moriarty is unbelievably determined to survive at any cost...
Moran spends several months hunting a seventeen-year-old girl. Considering that he spent over two years hunting Holmes, however, the surprise is not that he kept up the hunt but that the hunt kept him up.
I would fight to to make that bright and innocent past our future again. Even if it means dashing myself against the evil and cruelty of this wasteland until there is nothing left of me. And then, when I am too broken to go on, I will float my dying body right down into the throat of the darkness and make it choke on me.
Or, you know, this could all end in sunshine and rainbows. No need to get pessimistic.
Hybrid Theory. Determination is sufficiently central to the magical system and core plot that little can be said without spoiling the whole thing, except for "Holy crap!" and "Did you just punch out <censored>?"
In Code Geass Mao Of The Deliverance, Mao definitely qualifies. He gambles, blackmails, steals, does drugs, flies through a frickin hurricane, takes on soldiers and terrorists and gets shot repeatedly all in his quest to save C.C. and be with her forever.
Takato , OH DEAR LORD TAKATO. If continuing to fight againgst a hoard of Mega level digimon. despite the fact that your clothes are literaly soaked in your own blood, and you are almost paralysed from your brain cells dying doesn't count as this, nothing does.
Daemon as well.
Takeru: "Daemon is an extremely powerful foe, and his power has increased in the past fifteen years. His anger and desire for vengeance makes him practically invincible, a berserk fighter who will do anything to win."
Takato: "But…my friends will never give up! Rika will never give up!"
In Dragon Age The Crown Of Thorns, the Wise Prince protagonist keeps on going and pulling one plan after another, even though the fact he grew up in a Deadly Decadent Court could have long ago turned him into a self-centered cynic. He also displayed a high physical resilience in the deep roads, up until he stumbled upon a certain someone else and finally decided to allow himself to faint after two days of no sleep, fighting, getting repeatedly injured, tried for fratricide that never happened, dragged through streets in chains, spat on and generally not having a very nice time.
In the Firefly fic Forward, Mal shows his canon tendencies, but on top of that there's Book, who pulls a You Shall Not Pass when defending River from Reavers. As the story progresses, River herself becomes one as well, up to the "Fourth Interlude" chapter, where little things like a bunch of cracked ribs or having a leg broken, getting shot in the stomach, and getting a concussion from a ricocheting bullet don't stop her from kicking ass.
Jericho has the eponymous narrator, Jericho, a stallion from the nation of Teutschland. He appears to be this, since he walked to Equestria, where the story begins, all the way from his homeland of Teutschland, which is across the world and several oceans from Equestria.
The Party Never Ended has the poor addle-sounding Derpy Hooves determined to fight the supernatural storm, no matter what. And the climax features a Battle in the Center of the Mind. In one corner, the entity that drove Luna into Nightmare Moon via Break the Cutie. In the other, Pinkie Pie with Twilight Sparkle helping. Then Rainbow Dash with Pinkie Pie helping. Then Pinkie Pie by herself. Break The Breaker Of Cuties, anypony?
In the Pony POV Series, the Mane Cast and their Sixth Ranger Trixie stop at nothing to defeat Nightmare Whisper, Fluttershy's Superpowered Evil Side, and save her from herself. By the end of the battle, Pinkie Pie and Applejack are severely cut up by glass (Pinkie Pie from being throw out of a glass window and Applejack from having glass daggers embedded in her back), Twilight and Rainbow Dash have both been sent dangerously close to the Despair Event Horizon, and Trixie has been electrocuted and broken one or more ribs. But the one who takes the cake is Rarity, who has her legs broken and keeps herself in the fight by moving her legs with telekinesis! And thenFluttercruel fights her way out of a Jury of the Damned, getting pretty much mauled by demonic creatures, to get back to help save Fluttershy. She then proceeds to tear the tubes connecting her to Nightmare Whisper out 'by hand, despite the agonizing pain it causes.
This is actually a distinct plot point from a "side story" (Alternate Universe, but declared part of the POV multiverse by Word of God). An alternate Discord notes that the Ponies of the "Reharmonized" timeline, "Would never give up, no matter how hopeless the situation."
Also happens with Queen Cadence in the Dark World Timeline. She promised Twilight Tragedy she'd redeem her, but was vaporized before she could. Five hundred years later, her spirit appears to Twilight when she's suffering a Villainous BSOD and helps guide her back to the light, just like she promised.
Dark World!Derpy. To put this in perspective, she endured 1000 years of living Hell so Discord would remove the curse from Dinky. She marched around Discord's palace, assaulted constantly by crows trying to eat Dinky, and according to Dinky herself, she never let them touch her]]. And she did this with crippled wings and legs''. Is it any wonder at all she becomes an Element of Loyalty? After she's healed by the redeemed six and Dinky is restored, this determination extends to protecting her new friends.
Sunset Shimmer, from Seven Days In Sunny June, is willing to face down date rape gangs, nightmarish unicorns and a death threat from Princess Celestia if it means saving those she loves.
Naruto in The Sealed Kunai. While fighting Hidan and Kakuzu, he holds Kakuzu inside his barrier trap jutsu for one full minute while being sympathetically mutilated by Hidan, who is specifically trying to break his handseal. It eventually lapses when Hidan actually stabs through his hand, but enough time was bought for help to arrive.
Ruby in the Gorn-laidenBlood Rose becomes one of these - of note is the end of chapter 22, where despite having lost both her legs and had most of the skin on her body burned off by an incendiary barrier, she starts crawling off to escape before her Healing Factor even begins to kick in.
[Holmes] would have died for a secret. But he will live now, for a friend.
Watson: "Porlock, there is no use in arguing the point. I shall search for Holmes. Whether you help me or not is your choice, but you shan't stop me — you have my word on that."
Wiggins: "Mum, I've been running that risk ever since I was a mite. I can't tell you what I'm doing, but I need to see it through. Peter's a fine young man, and he'll take good care of you. I'll come back if I can, I promise."
Optimus and Starscream in Hate the Dark, but mostly Optimus.
Eugenesis has Galvatron. Imprisoned, damaged and implanted with technology designed to prevent him from transforming ever again, Galvatron still manages to break free, and more importantly, transform, utterly ignoring the fact that the pain and strain of doing so hurts more than anything he's ever experienced.