Supergirl is the Trope Codifier. Although not the first female copy of an established hero (Mary Marvel and Bulletgirl preceded her), she has had the most longevity and the most incarnations, including her own movie and live-action show.
Power Girl, being originally Supergirl's alternate universe counterpart before Crisis on Infinite Earths brought her to the main DCU, is also a distaff counterpart of Superman.
During the Post-Crisis continuity, Power Girl got her own spear counterpart in the form of Power Boy, complete with a version of her infamous Cleavage Window. His only notable storyline featured him acting like an abusive boyfriend to Supergirl, and he ultimately became C-List Fodder and hasn't been heard from since (outside of a few appearances in Tiny Titans).
In Last Daughter of Krypton, a significant addition to Supergirl's Rogues Gallery has the distinction of being the Distaff Counterpart to two major Superman foes- Reign has a very Doomsday-like originnote a Super-Soldier created on Krypton from an alien infant, Gone Horribly Right, and a very Zod-like personalitynote Smug Super conquerer with a personal vendetta against the protagonist's family, deeply driven to make said protagonist submit to them. Incidentally, she basically presents herself as Kara's Evil Counterpart as well.
Element Girl, the female Metamorpho. She is mostly known for being saved by Death from a sad and lonely existence in The Sandman. Since then she has made another appearance outside of DC continuity in Wednesday Comics.[1] The concept has since been recycled in the form of Element Woman, a new Korean American successor to Element Girl.
Aquagirl, the female equivalent of Aquaman's sidekick Aqualad.
The Joker has Harley Quinn, while the Riddler had a short-lived female counterpart named Quelle.
Before Quelle, Riddler had a pair of female associates named Query and Echo.
It gets a bit confusing when you consider that Earth 11 features Gender Flip versions of characters that already HAVE Distaff Counterparts, or who already ARE distaff Counterparts. For example; Superlad.
The Ame-Comi Girls universe features most of the primary hero roles in the hands of the usual female distaff counterparts. So Jesse Chambers is The Flash, Carrie Kelly is Robin, Natasha Irons is Steel, etc.
Metal Men Issue 32 features a story called "The Metal Women Blues", where the team gets jealous of Tin and Nameless and get their creator, Will Magnus, to create opposite sex counterparts for them. During the subsequent mission, a rift grows between the males (Gold, Iron, Lead, Tin, Mercury, and Platinum Man) and females (Gold Girl, Iron Girl, Lead Girl, Nameless, Mercury Girl, and Platinum). The Metal Women eventually rescue the Metal Men from Robot Amazons, but they were unable to rescue Platinum Man from falling into the Earth's core, and all of the Metal Woman except Platinum and Nameless end up perishing along with him.
Zatanna, the daughter of Zatara. Rare case where the distaff counterpart completely overshadowed the original in terms of popularity.
"Roberta the Girl Wonder" (Mary Wills) was the first female Robin counterpart debuting in 1950, eleven years before the first Batgirl Bette Kane (though unlike Bat-Girl, she only made a single appearance). Carrie Kelly, the Robin from The Dark Knight Returns is an even more straight example. Stephanie "Spoiler" Brown's brief run as Robin where she became the title character of Robin (1993) for two issues may also count.
Jonah Hex (2005): Tallulah Black. Like Hex, she's a physically and mentally scarred individual with absolutely nothing to lose.
Miss Martian to Martian Manhunter. Notable in being one of the few superheroine distaff counterparts whose costume covers more than the male version; Miss Martian wears a Sailor Moon style outfit, which covers quite a bit more than "two leather straps and a speedo." In personality she started as pretty much an Expy of the animated Teen Titans Starfire.
On the subject of distaff counterparts with a more concealing costume: Bombshell to Captain Atom. Bombshell wears a t-shirt and trousers, while Captain Atom is effectively naked.
Natasha Irons started off as the replacement Steel when her uncle John took a break from his Powered Armor. She ended up changing her Code Name to Vaporlock after gaining her own powers.
Batwoman was introduced as a distaff for Batman back in 1956 (as well as to quell some vicious rumors circulating about Batman and his young ward), serving as a feminine counterpart to his crime-fighting adventures (using "feminine intuition" and having cosmetic-themed gadgetry, for example). When she was re-introduced in 2007's 52 and given the lead role in Detective Comics her personality and history were updated. The Cutter arc of Detective Comics goes into an explicit examination of the parallels between the two characters, with alternating pages (And sometimes even alternating panels) following both characters as they each tracked a separate criminal (eventually revealed to be the same criminal, but the Batman scenes were about five years earlier), each one going through the same motions, victories and setbacks as the other.
In the Silver Age, DC Comics had a character called Johnny DC, who would tell kids about upcoming books. In Ambush Bug this character gets reinvented as Jonni DC, Continuity Cop.
Wonder Woman (1942): Very, very briefly Steve Trevor became a costumed superhero to act as Wonder Woman's male counterpart as Captain Wonder. The whole thing turned out to be a villain plot to depower Diana so he quickly ditched the powers and ID.
The Flash: Naturally as a Legacy Character, there's a few female speedsters to counterpart the male speedsters.
The most prominent and well-known is Jesse Chambers, AKA Jesse Quick, and is most-explicitly a Distaff to Wally West (being a legacy character with "Well Done, Son" Guy issues who idolised the character they're a legacy of), though she's actually a Distaff Counterpart to her father, minor Golden Age hero Jack Chambers/Johnny Quick. As she was introduced right before the Flash Family began to primarily act as an Identically Powered Team, she served as somewhere between The Heart and The Lancer of the team.
Before her, Christina Alexandrova/Lady Flash was the first real one (prior, a one-off Silver Age story that was All Just a Dream had Mrs Flash/Patty Spivot), though she was also a Shadow Archetype and eventually become a full-fledged villain.
The Flash (2016) added two more, in the form of Avery Ho, The Flash of China (who specifically acted as Wallace West/Kid Flash III's Distaff), and Fast Track/Negative Flash, who acted as Barry's Distaff (right down to being a Science Hero and mentor figure), and also briefly a Shadow Archetype like Christina (though in her case, it was Brainwashed and Crazy).
Green Lantern: Though there's been many alien Lanterns who happened to be women, the 2010s saw the franchise introduce Jessica Cruz. She wears a costume that is almost identical to Hal Jordan's (with minor differences, though interestingly not in any ways that make it more feminine or stripperific, and she acts as The Heart during Bat Family Crossover moments.
Before her, Jennifer-Lynn 'Jenni' Hayden/Jade was the daughter of the original Golden Age Green Lantern, Alan Scott, and her powers are derived from the same source as his, though she has been inducted into the Corps proper and briefly lived with/dated Kyle Rayner.
Teen Titans (Rebirth) introduced Lobo's illegitimate teenage daughter, Crush, who is an anti-authoritarian Blood Knight, yet her morality leans closer towards heroic than Lobo's.
The concept has since been recycled in the form of Element Woman, a new Korean American successor to Element Girl.