An issue of Ambush Bug from the 1980s once listed a bunch of corny Silver Age characters that should never be mentioned again because they could not possibly work in modern comics. Grant Morrison has since made them all awesome.
Although the process was aided by her gaining vampiric powers, Pearl Jones from American Vampire comes under this trope. After being victimized by a coven of "traditional" vampires, and turned into a vampire by Skinner Sweet on a whim, she goes on a Roaring Rampage of Revenge against her tormentors, and becomes a Violently Protective Girlfriend to her chosen man, who is a retired Semper Fi/Marine and no pushover in his own right.
For the last several years, DC has been trying awfully hard to shake the famous notion that Super Friends put forth about Aquaman that he's useless outside of his ability to talk to fish. A lot of his appearances try a bit too hard to show off what a rugged badass he is to the point that he may as well have a neon sign over his sign reading "Do you guys think I'm badass yet? Guys? Please?" Although comic book readers know that he's come a long way since his Super Friends incarnation, the mainstream was unfortunately yet to care or notice; you could still catch the stock "Aquaman is useless" joke from time to time. However, the outstanding success of the DCEUfilm adaptation of the character in 2018 has quelled much of that, embracing the quirkier elements of the character to win the public over at what a thrilling badass hero he is.
Jason Todd (Robin II), when he became the second Red Hood, deserves a mention as well.
Tim Drake (Robin III), started out with the least crimefighting applicable skills out of all the Robins prior to his training and leveled up by training with Lady Shiva to become a Hyper-Competent Sidekick. By the time he took on the identity of Red Robin when his former title was taken from him he was among the most dangerous and competent non-powered heroes in the DCU due to his analytical mind, connections and staff fighting skills.
Black Mask was a D-list villain (Batman sent "Batgirl" (Huntress) to defeat him in No Man's Land), then came "War Games"; at the end of that mini series, Black Mask became crime lord of Gotham City.
In Convergence Booster Gold #2, Booster Gold was dying due to leaving pieces of himself through time and Rip Hunter had an idea. He took Pre-Zero Hour: Crisis in Time! Blue Beetle, Pre-Flashpoint Michelle Carter and New 52 Booster Gold to Vanishing Point in an attempt to save the dying Booster. He had New 52 Booster take dying Booster into a secret room and leave him to be merged with the time stream. When he emerged he was the new Waverider. Booster, Waverider and Rip Hunter were then instrumental in saving and restoring the multiverse at the conclusion of Convergence.
Snow White, in Fables, certainly qualifies. She started out as a helpless, hunted girl, spent years as a sex slave for seven perverted dwarfs, and eventually became one of the most badass people in a comic full of them. The first indication that the times, they were a-changin' was when she learned swordplay from her husband...and went on a Roaring Rampage of Revenge against the dwarfs, nearly setting off a human-dwarf war.
Grunge of the newly rebooted Gen¹³ series is a slightly different example. He starts out as your more-than-average nerd with genius IQ and photographic memory. And the first name... Percy. So he starts working out, hides his book smarts and his photographic memory, starts using his middle name, trains in martial arts and starts skateboarding. And turns into a stereotypical 'stupid' musclebound frat boy slacker by the start of the series when we first see him. And then he gets superpowers.
In Final Crisis Aftermath: Run!, the Human Flame, an incompetent villain who usually kills people by accident, gets tired of being a joke villain and decides to take so many levels in badass that he will never have to run away again. Ultimately subverted, as he takes too many of them and ends as a monster so big, that he cannot move under his own weight.
Seems to be standard for a character when they're managed by Geoff Johns. The revamping of throwaway Green Lantern villain Black Hand is a prime example, with his pivotal role in the Blackest Night series.
In the Villains United and Secret Six comics, former Batman whipping boy Catman has graduated to a capable threat, fighting the Caped Crusader to a standstill in one issue.
Just to give you an idea how big the change was, the last time we saw Catman before Villains United was Archer's Quest where he was a fat slab doing grunt work for the Shade. First scene with him in Villains United has him, very fit, leading a pride of lions and telling the Secret Society of Super Villains where they could put their recruitment drive.
This is more a case of Rescued from the Scrappy Heap. When he first showed up in the Silver Age, Catman was a skilled fighter who took on Batman and nearly won. Later writers just made him more and more pathetic (the crowning example would be Green Lantern 80-Page Giant #1, in which he is captured by G'Nort. A ringless G'Nort).
Supergirl increased her badassery in the Red Daughter of Krypton storyline when she got a Red Lantern Ring. Lantern Rings are the most powerful weapons in the universe, and Red Rings are fueled by their bearer's fury. And Supergirl is a headstrong, Hot-BloodedKryptonian.
In Trinity (2008) Kara becomes a highly-trained government agent Interceptor in an alternate reality.
DC crossover Underworld Unleashed Nero offers to grant wishes in exchange for souls and makes this deal available to the villains first. Many of them use this opportunity to take levels in badass. For example, Blockbuster, a big dumb guy, wished to be a Genius Bruiser and eventually ended up as the crimelord of Bludhaven in the Nightwing title years later.
Yorick in Y: The Last Man starts as an inept loser who's often beaten up by women (including his sister) but with the help of some traumatic incidents, and training by Agent 355, becomes more adept at defending himself. Subverted also in one scene when a non-action character suddenly whips out a sword in an apparent elevation to Badass, only to be easily defeated by the more experienced villain.
