Badass Normal/Fan Works

BlackDragon6's Ranma ½ story Guardian features a character named Ken "Snake" Yakata, a Jewish gun nut who is routinely billed as the most deadly fighter in the Department of Abnormal Phenomenae Containment with the sole exception of Ranma. This is in spite of the fact his other officers are: a powerful psychic psycho capable of cutting the heads off powerful vampires, a superhuman capable of going toe to toe with cyborgs and the worst boss enemies in the Resident Evil series, and a bloody Zergling. All Snake has is a shotgun.
- To further emphasise the extent of this, it should be mentioned that Snake terrifies every single one of his fellow officers, save Ranma. To an extent, anyway. They know he can't shoot them and thus they feel somewhat secure around him, but around his evil clones they are terrified.
Balian of Ibelin in The Chance Encounter series. While he has been rendered immortal, this only seems to prevent him falling ill or indeed ageing. He also fights alongside Achilles, Legolas and Will Turner (during his "undead captain of the Flying Dutchman" period) and holds his own easily. When he is briefly turned evil by dark magic, he even forces LEGOLAS into retreat. He also takes on many of King Richard I's soldiers at once and wins, with the King's spymaster not sure if the King (who was a noted warrior himself) would survive a head to head confrontation. Oh yes, and he wades through HELL ITSELF to save his dead-by-suicide wife, taking on Satan and...mostly getting the crap beaten out of him actually, but he stood up to the ultimate evil and survived!
Author Avatar Art of the Mass Effect self-insert Mass Vexations eventually becomes a good Soldier-class unit within Shepard's squad. This seems to fall into Badass Abnormal territory until you realize that he never got any of the genetic implants that most soldier-class units get in the Mass Effect universe. He also Took a Level in Badass considering he had never fired a gun in his life before entering the Mass Effect universe.
In the Transformers fic, They Just Don't Care Anymore, the character Alien spends a lot of time being criticized as a minor character who won't get to do anything important and will inevitably be the first to die when a horde of undead attacks... until a horde of undead actually attacks. In a Crowning Moment of Awesome, she announces that she's sick of being called a minor character, whips out a pair of kukris and single handedly takes down everything in her path, after which she proceeds to throw a guy into a quarry because he annoyed her.
Tuxedo Kamen manages to pull this off in this chapter of Takamichi Nanoha of 2814 (keeping in mind that this is the rose only version of the character) when he goes toe to toe with Signum using a sword-cane. To put this in context, Signum and the other Wolfenkritter had previously managed to stand up to the combined forces of every other character, including some big names like the Sailor Senshi, Negi Springfield and co., Sakura Kinimoto and Syaoran Lee, Nanoha, Fate, Yuuno and the combined might of the TSAB and Superman. Yeah.
Poke Wars has Samurai, a Pokémon trainer who lost his Pokémon early on in the war. Yet, he is more than capable of holding his own in a fight against them with only his katana.
- Lt. Surge also counts. He was able to hold off a group of Electivire and Scizor with only a combat knife.
Gwenith Cousland and Theron Mahariel in the Dragon Age fanfiction Dragon Age: The Crown of Thorns qualify, although the latter's very sharp hearing could be seen as a Charles Atlas Superpower in its own right. Of course, seeing as how everyone else, especially Kallian Tabris, either came with or gained some power or another over the course of the story, it is unclear if this status will last for the human noble and Dalish. Leliana and Zevran still fit perfectly though,
Tatsu no Houho from the Tamers Forever Series is shown to be able to take on several ultimate level digimon with nothing but a Katana
- Takeru has a similar scene later on
Cloud Kicker from Ace Combat: The Equestrian War doesn't have a Signature Move like Lightning Bolt, is not as fast as Firefly or Rainbow Dash and she still manages to kick griffins' butts.