Bunnie D'Coolette (Sonic SatAM/Archie's Sonic the Hedgehog)
Toph Beifong (Avatar: The Last Airbender) is one of the greatest Earthbenders in the world despite being born blind.
Even after losing his left arm and right eye during the Eclipse, Guts (Berserk)...
...is still a capable swordsman...
...growing stronger with his handicaps after becoming the Blackswordsman.
Despite her handicap, Tsukuyo Inaba (Busou Shoujo Machiavellianism) is a master swordswoman. She can easily match, defeat, and nearly kill Fudo Nomura in combat almost effortlessly.
With no arms, the Armless Sensei (DC Comics) was a master martial arts who taught a great many pupils the art of combat.
The brother of the Armless Master, the Legless Master (DC Comics) was a great martial artist.
Acnologia (Fairy Tail), after losing his arm to Igneel.
As a member of the Yonko/Four Emperors of the New World, Red Hair Shanks (One Piece) is still one of the most powerful pirates in the world...
...the loss of his left arm not hindering him in the slightest.
With a massive golden hook, Crocodile (One Piece) makes up for losing his left hand, wielding it with powerful proficiency.
Even after the loss of his left eye, Rororna Zoro (One Piece) is still a powerful and skilled swordsman...
...his handicap not hindering him in the slightest.
Admiral Issho/Fujitora (One Piece)
Despite chopping off his own left leg, Kyros (One Piece) still retains his incredible swordsmanship and agility.
Eustass Captian Kid (One Piece)
By his own admission, Sesshomaru (Inuyasha) actually became significantly more powerful after losing his left arm to his brother, InuYasha.
Big Boss (Metal Gear) was unhindered by the loss of his left eye and was also able to embark on Operation Snake Eater and successfully complete his mission despite having suffered numerous severe injuries only a week earlier.
Neo (The Matrix) remains a skilled martial artist despite having his eyes cauterized by Smith.
Joker (Mass Effect) is a master pilot despite suffering from severe Vrolik's syndrome in his legs.
Even when his arms were incapacitated, Zabuza Momochi (Naruto) killed most of Gato's thugs and Gato himself with only a kunai in his mouth.
Despite both of his arms being torn off, Deidara (Naruto) was able to hold his own against Team Guy, until Kakuzu reattached his arms.
Despite having his left arm burned off by Sasuke Uchiha's Amaterasu, Fourth Raikage Ay/A (Naruto) was still a challenging ninja.
Nagato (Naruto), after his legs were damaged by an explosion.
Despite losing his left arm during his final duel with Naruto Uzumaki, Sasuke Uchiha (Naruto/Boruto: Naruto Next Generations) is still one of the most powerful ninjas in the world.
Matt Murdock/Daredevil (Marvel Comics)
Master Izo (Marvel Comics)
Despite being partially deaf from childhood, Clint Barton/Hawkeye (Marvel Comics) was able to successfully become a master archer and martial artist.
The perfect example of the blind swordsman, Zatoichi (The Tale of Zatoichi) is a supremely skilled swordsman despite being blind.
Despite being paralyzed from the waist down, Joe Swanson (Family Guy) was able to remain on the police force and takedown criminals even though being in a wheelchair.
After being rendered a paraplegic by Clock-La, Bentley (Sly Cooper) remains a capable field agent due in part to a high-tech wheelchair.
Desitpe being left a paraplegic after getting shot, Johnny Joestar (JoJo's Bizarre Adventure Part 7: Steel Ball Run) was still able to maintain his skills and prowess as a world-class horse jockey before learning about the Spin.
After sewing his eyes shut, Uzu Sanageyama's (Kill la Kill) enhanced his senses affinity with his Goku Uniform, allowing him to sense the area all around him, claiming to see the entire world.
All-Rounder General Kou Son Ryuu (Kingdom) is one of the State of Zhao's deadliest generals despite having lost the use of his left eye.
Despite having lost his left eye in his youth, Ryuu Tou the Left Hand of Ki Sui (Kingdom) was a powerful tactician and capable warrior.
After losing his fingers, Rin Ko of the Four Heavenly Kings (Kingdom) compensated the loss with his acute horsemanship.
Despite missing an arm and a leg, Gobber the Belch (How to Train Your Dragon) is just as capable of smithing and battle as the rest of his tribe.
Hiccup Horrendous Haddock III (How to Train Your Dragon), despite missing a leg, is able to accomplish many feats, including his unmatched skills at dragon-riding, combat, and smithing.
Despite born without fangs and have no limbs, Viper (Kung Fu Panda), is able to fight.
Despite her broken horn, Fizzlepop Berrytwist/Tempest Shadow (My Little Pony: Friendship is Magic) is still able to use magic.
Edward Elric (Fullmetal Alchemist)
Despite born blind, Hattori Tatsu (Teenage Mutant Ninja Turtles 2012 TV series) has some enhanced senses.
Ashley "Ash" J. Williams (The Evil Dead series)