The Karate Kid (DC Comics) possesses such skill in martial arts that he can damage solid rock and metal, as well as briefly hold his own against Kryptonians.
Karnak Mander-Azur (Marvel Comics) is the only inhuman who did not undergo terrigenesis as he came of age, all his powers and abilities come from decades of intense physical and mental strengthening regimens he partook throughout his life.
Through The Hercules Method, Luther Strode (The Strange Talent of Luther Strode) developed physical and mental abilities beyond any normal human.
Hayley Smith (American Dad!) is a sleeper agent from Project Daycare, trained to be an unstoppable killing machine, in which she proved in her attempt at her father's life upon her programming malfunction.
After his home was taken over by Aku, Jack (Samurai Jack) was sent by the plan of his parents to undergo various forms of training by the greatest and most renowned warriors and scholars of the world and became an incredibly skilled and powerful warrior as a result.
Bucky Barnes (Marvel Comics) received training in Hand to Hand combat, Reconnaissance and surveillance in hostile environments, Marksmanship.
....and combat training from from S.A.S veterans during the early days of WWII.
Bruce Wayne (DC Comics)
Dick Grayson (DC Comics)
The X-Men (Marvel Comics) training daily inside of the Danger Room.
Having been trained as a mercenary since age six, Guts (Berserk) possesses incredible physical capabilities, able to easily wield a massive 400-lb sword with one arm, move faster than the eye can see, and survive wounds that would be fatal to a normal man.
Sn Goku (Dragon Ball series) was taught by Grandpa Gohan the basics of martial arts, by Korin in endurance and opponent anticipation, by Master Roshi in Kame-Sennin Ryu to push his body to superhuman levels, by Mr. Popo and Kami in ki sensing, mediation, precision, and Bukūjutsu, and by North Kai in ki training, the Kaio-ken and Spirit Bomb.
Master Roshi (Dragon Ball series) achieved superhuman status through training, to the extent that he was once hailed the strongest man in the world.
Though nowhere near the Z-Fighters' level, Hercule (Dragon Ball series) is nonetheless more powerful than an ordinary human thanks to his training, able to pull off such feats as moving faster than the eye can see, pulling a line of four buses several feet with his bare hands, and surviving hits from Perfect Cell and Kid Buu.
Even without his Devil Fruit powers, Monkey D. Luffy (One Piece) possesses incredible strength and skill as a result of a training regimen his grandfather put him through.
Those who practice Hokuto Shinken (Fist of the North Star) train to unlock and use their bodies' full muscle potential.
Genkai (YuYu Hakusho) is an incredibly skilled martial artist known to humans and demons alike. Her personal Reihado-ken fighting style allows her to revert her body its peak. She is also a harsh teacher with grueling, but beneficial, training methods.
Yusuke Urameshi (YuYu Hakusho) went through hard training under the teachings of Genkai, but in turn was able to learn the Spirit Shotgun, Spirit Wave, and had his Spirit Energy greatly improved by the aid of her Spirit Cuffs.
Shinobu Sensui (YuYu Hakusho) is a master of the Resshūken fighting style, which is said to be to be the strongest, most elegant, school of martial arts in existence. In addition to this, he was able to master the Sacred Energy with only six years of discipline instead of the usual forty.
Even in old age, Walter C. Dornez (Hellsing) possesses superhuman speed and acrobatic skills due to years of training and experience.
Akisame Koetsuji (History's Strongest Disciple Kenichi) has trained his body to that point that he has absolutely no unnecessary/useless muscle, as every single inch of his frame is composed of only pink muscle. Granting him nearly superhuman skills equal to the Elder.
Saitama (One-Punch Man) broke through his human limitations and achieved unbelievable strength and abilities considered impossible through an extensive training regimen.
While originally the weakest Issei Hyodou (Highschool DxD) became the strongest reincarnated Devil of his generation through constant and rigorous training.
Cao Cao (Highschool DxD) has trained his body and fighting skills to utmost perfection, making him strong enough to defeat the most powerful supernatural beings.
The Vizards (Bleach) underwent hard training to fully control their new found Hollow powers after being forcefully modified into Hollow Hybrids.
In order to attain longevity, Honest (Akame ga Kill) has rigorously trained his body to complete perfection...
gaining immense strength and fighting skills to single-handedly overpower a Teigu user.
Sword Emperor Elline (Sekai no Owari no Encore) attained his legendary swordsmanship skills through extremely hard training.
Through four months of rigorous training, Frieza (Dragon Ball) became the first of his kind to awaken the Ultimate Evolution.
After two years of extremely rigorous training, Monkey D. Luffy, Roronoa Zoro and Vinsmoke Sanji (One Piece) became tremendously powerful, able to survive the dangers of the New World.
Jann Lee (Dead or Alive series) is strong enough through training to beat a T-Rex unconscious with his bare hands.
Through training, Solid Snake (Metal Gear series) is able to pull off feats such as dodging bullets from multiple ranges and withstanding electrical torture.
Ryu (Ninja Gaiden series) attain immense physical prowess and tremendous combat skills through extremely rigorous training since childhood.
In shown in multiple incarnations, Link (The Legend of Zelda seires) learned incredible sword techniques from either training under certain masters or learning from scrolls. Aside from his swordsmanship, most incarnations of Link have acquired skills in hand to hand combat from his hometown.
Through extensive physical training, Chris Redfield (Resident Evil series) possesses sufficient strength to move boulders several times his own height and weight, and hold his own against superhuman beings like B.O.W.s and Albert Wesker.
Segata Sanshiro (Sega) has trained so extensively in martial arts that he can pull of a variety of superhuman/supernatural feats, such as causing those he throws to explode on impact with the ground, kick a baseball for a home run, and survive in the vacuum of space unaided.
Ryu (Street Fighter series) has trained extensively in the Ansatsuken fighting style under Gouken, bestowing such abilities as ki manipulation.
Though elderly, Heihachi Mishima (Tekken series) possesses incredible strength and electrical powers due to his training in Mishima-Style Fighting Karate.