Super Robot Wars tends to do this quite a bit. Boss and his Boss Borot originally were Joke Character tier in the early games, but by the Alpha series had upgraded to low-medium usefulness, and by the J/W/K/L handheld era he got very good if not outstanding. Bright Noah, already badass in his own right and a competent ship captain in the early games only got better to the point that he can take down Angels.
The explanation for Boss is the fact that, by the time of J, they've went from the original anime to Mazinkaiser and Shin Mazinger.
Taizo Hori, hero of the original Dig Dug, and member of the Mr. Driller cast, pictured on the main page in his appearance in Namco × Capcom. Besides changing his look to one that's more realistic and rugged, the game also altered his background so that he's a former soldier in addition to being a digger. Actually, Namco × Capcom has a lot of this.
Ditto for Hudson's Bomberman and Lode Runner. Although you'll never see Lode Runner's new look without playing the cell phone version of this game. And, after all, new Lode Runner will look like a kid. Yeah...
Sierra, on the other hand, made him look like a more matured adventurer.
In Warhammer 40,000, the Tau Fire Warrior is a basic grunt unit. When adapted to Fire Warrior, the eponymous Tau grunt is able to single-handedly take on the forces of Chaos, and be able to take out several contingents of the Emperor's finest Space Marines. The novel, however, delves into some of the Tau lore and explains it a bit better: Kais is fighting a different battle, only his enemy is the very warlike and self destructive aspect that pushed the Tau to the verge of extinction that they thought they no longer had to worry about. His mentor explains that it is something every Fire Warrior has to face and come to grips with.
In the prequel, Laguna Loire also got this treatment. In his original game, he wasn't particularly special in combat, he fired a couple blasts from his trademark machine gun as his normal attack and for a Limit Break threw a grenade and fired his machine gun double-time. In Dissidia 012? He's the living embodiment of More Dakka, packing rocket launchers, a machine gun, various types of grenade, a sniper rifle, and a giant laser cannon in the shape of the airship Ragnarok. And his Limit Break? Calling all his weapons together to form a Wave Motion Gun.
One of the largest upgrades happens in Final Fantasy VII with spells. Meteor and Holy had been recurring powerful Black and White spells, respectively. In the seventh installment they are boosted far beyond that to plot devices as the Black and White Materia and were capable of wiping out or defending the entire planet. The series-wide reference was lost for most western audiences due to the then lack of previous installments and inconsistent translation.note Holy was renamed to Fade, White, and Pearl in the three that made it over.
Donald goes from a short tempered household name to a Badass Abnormal, Goofy is a Badass Normal who fight just as well as the characters WITH magic. Minnie may also count but we only get so little out of that escort mission in Kingdom Hearts II.
Of course, this is just an expansion of the currently underutilized in America side of Mickey as a great adventurer. Comics have always been a place for his badass side to shine, especially in Italy.
In Wonderland at least, in the second game it's driven home that in the real world, Alice faces the very real dangers of being a mentally unstable teenage girl in Industrial Revolution London.
The Hobbit from 2003 does this to Bilbo. Sure, he doesn't get to fight trolls or dragons but he can fight hordes of goblins, giant spiders, the undead and liches. He can break enemy shields with his sword, and create a shockwave on the floor with his walking stick that sends enemies flying. And he can pole vault with the stick too.
The guy from Minecraft (who's apparently named Steve? (? included)) got this kind of treatment in his cameo appearance in the PC version of Super Meat Boy. Just like in Minecraft Steve? can both lay blocks in the game world as well as dig through anything, making the usually challenging platforming game comically easy. Essentially this ability goes so far beyond game breaking that Steve? is basically bending the game over a table and having his way with it.
Bumblebee in his Transformers: War for Cybertron incarnation is a Hot-Blooded playable character who can easily rack up a triple-digit kill count over the course of the Autobot campaign. He doesn't have the raw power of Optimus Prime but he makes up for it with speed, skill and determination.
Some of the gods in God of War are depicted are being much stronger than the Greek Myths presented them as. Ares, the Big Bad of the first game, is presented as a titanic warrior the requires a MacGuffin for Kratos to have a fighting chance against, where in the Greek myths he was a coward that would run away from a fight at the first sign of trouble despite being immortal (though Ares as an Adaptational Badass is also done in every other adaption of him—including Roman mythology), and Persephone in Chains of Olympus, who was simply mentioned as being dragged off by Hades in the Greek myths, is presented as being able to fight Kratos in hand-to-hand combat.
Fist of the North Star: Ken's Rage featured Mamiya as a full playable character. In the series, she was shown to be reasonably affective against small groups of Mooks, but against large forces or serious Martial Artist types, she'd inevitably turn into a Distressed Damsel in need of rescuing. Being a playable character, however, means that she's now fighting on par with Kenshiro himself - tearing through armies of hundreds if not thousands, and singlehandedly disassembling top-tier bosses. It probably helps that she's picked up an Automatic Crossbow somewhere - heck, she can even pull a SECOND one out of Hammer Space for one of her Signature Moves.
Liu Shan in the original Romance of the Three Kingdoms is the definition of Suck Sessor, completely inept at fighting and ruling, and in the first sight of danger, he surrenders. Dynasty Warriors turns him into an actually Badass Pacifist by the virtue of being playable. Not exactly top tier, but much more competent, savvy and in a way, virtuous like his dad, although he's a bit scatterbrained (or so he presents himself to public). On the assault on Cheng Du, he fought against Sima Zhao first before retreating, rather than surrendering on sight. Only after their next encounter he surrenders. note And the reason he surrenders wasn't because he's scared as hell, but to preserve the people of Shu from the Hopeless War brought forth by his subordinates who simply doesn't know when to quit. In 8, the implication of Hopeless War and 'subordinates who doesn't know when to quit' is absent, but Liu Shan still fought Sima Zhao as the latter enters the throne room to the end before surrendering.
Arthur from Ghosts N Goblins is a little guy in a suit of armor. When he appeared in Cannon Spike, he notably was changed into a giant, muscular weapon of destruction.
Jack Driscoll in the 2005 version of King Kong was a pretty meek guy whose every attempt at being heroic always inevitably failed. In the corresponding video game, however, he's the human Player Character. Despite having no military training, he wields a variety of firearms, can throw spears like a pro, and kills all sorts of dinosaurs and monsters before getting off the island.
When Freddy Krueger first showed up in Mortal Kombat 9 he seemed like more of an Adaptational Wimp, having lost most of his supernatural powers and being forced to rely almost entirely on his Wolverine Claws to fight. Then you remember that he only has his powers in the dream world while in the physical world he's pretty much just a foul-tempered burn victim with knives on his hands. In the movies, getting dragged into the physical world is basically a death sentence for Freddy, as the first movie in the franchise showed us he can't even outfight an untrained teenage girl in the real world. So watching him hold his own against people like Liu-Kang and Shang Tsung without his nightmare powers is actually pretty incredible.
Bass.EXE from the Mega Man Battle Network series. when compared to Bass from the classic series, he went from a somewhat challenging rival of Mega Man to theBonus Boss of the franchise, and with good reason. He is also considerably more unhinged than in the Original series.
Injustice: Gods Among Us: Characters like Batman are shown being able to survive being punched into orbit thanks to competitive balance. In-universe, it's the use of Kryptonian nanomachines that handwaves Badass Normal characters being able to fight toe-to-toe with Superman.
Dynasty Warriors: Gundam turns a few notable Gundam characters into this, most notable Elle Vianno, who was pretty inept with the Gundam Mk-II, and Lacus Clyne, whose only moment of piloting a Mobile Suit was guiding the Infinite Justice down to Earth.