Bane was designed explicitly as a total package villain: a ruthless criminal with both superhuman strength and a genius intellect that rivaled Batman's own. Adaptations have not always been kind to the character, sometimes making him a Dumb Muscle instead, but The Dark Knight Rises and Batman: Arkham Origins provided the definitive adaptations.
Batman’s various sidekicks/adoptive children also fit the bill being all great detectives and peak human martial artists. Among them Barbara and Tim are considered the smartest though are no less strong being able to take on the residents of Apokolips and come back alive. Jason and Cassandra are considered the physically strongest (the former thanks to Venom) but are also keenly intelligent. Dick Grayson being the first sidekick takes after his adoptee mentor the most so therefore has the best balance of brains and brawn.
Killer Croc was this in his very early appearances having both greatly enhanced strength and a scaly hide as well being surprisingly clever being able to get the jump on Batman and even outwit him. Unfortunately for Croc his Badass Decay came in thick and fast soon after and he’s been written to be savage animal who gets beaten up easily for the majority of his appearances since. Only a select handful of comics such as Batman: Earth One and Suicide Squad and Redhood And The Outlaws reestablish the fact he’s actually a case of Smarter Than They Look.
Mr. Freeze in addition to being a genius cryogenicist is incredibly formidable in a fight thanks to his cryo-suit that keeps his body cool doubling as Powered Armour that greatly increases his strength. He’s been able to give Batman a helluva a fight multiple times in many different continuities and when teaming up with the Dark Knight they prove to be a devastating duo.
Clayface surprisingly is a case of this Depending on the Writer, being a shapeshifter he’s remarkably cunning and at times quite ingenious with the weapons and people he can turn his body into. His strength is also insane being able to beat up even the likes of Wonder Woman and Supergirl with former being due to the fact he researched Diana learned she was made from Clay (this was pre-Semi-Divine retcon) and absorbs her essence to become massively stronger. As he says himself “A good actor always does their homework”. Averted at other times where he’s just a dumbass Blob Monster though.
"Hardback" Bock, a Scary Black Man Gotham police detective, who gets his nickname because he's always carrying one.
The criminal robotic and cybernetics expert Nathan Finch, aka Gearhead. When his kidnap scheme is foiled by Batman, an accident leaves him a quadruple amputee; he later develops incredibly powerful cybernetic limbs, and comes gunning for revenge against the hero, now a physical match even for Batman because of them.
Kate Kane is a highly educated and ranking former West Point cadet, knows over a dozen forms of martial arts, is a multilinguist, and has training from the likes of the FBI, SAS, SEALs, and Green Berets, among others.
Recurring Silver Age Private Investigator Hugh Rankin is a quick-fisted brawler, but is no fool. He comes up with a Batman Gambit to get Elongated Man to help him close a case and nearly figures out what Batman looks like under his mask through forensic science.
Brainiac. Since 2000 (with Brainiac 13) and continuing to the present (with the "true" Coluan cyborg Brainiac) Brainiac has consistently been shown to be Superman's physical superior, able to manhandle the Man of Steel with little effort. This makes him one of the most physically powerful beings in the DCU, possibly even stronger than the likes of Darkseid (Depending on the Writer in regards to how the latter compares to Superman). His true form is also about seven feet tall and built like a super heavyweight MMA fighter. But it speaks to his immense power that his physical strength is probably the least dangerous thing about him: as a "12th-level intellect", he's the smartest being in the DCU bar none (for comparison, the entirety of 21st century Earth's population amounts to a 6th-level intellect). His brain is capable of storing and processing octodecillions of minds worth of information (which he has, in the process of assimilating the many civilizations he's destroyed) and grants him superhuman calculation abilities, enhanced memory, and advanced understanding of mechanical engineering, bio-engineering, artificial intelligence, physics and other theoretical and applied sciences. He has invented tech that lets him shrinking entire planets, create impenetrable force fields,note In the New Krypton arc, Zod tries to destroy his ship with a Kryptonian super-weapon. The weapon does zero damage to the ship on part of Brainiac's forcefield, but the collateral alone flat-out kills hundreds of Superman-level Kryptonians who were standing nearby., transfer his mind digitally, and travel through time. This is on top of being The Chessmaster and creating armies of robotic bodies that are each able to rival and even kill Kryptonians.
A Golden AgeCaptain Marvel villain called King Kull (not related to the Robert E. Howard character), a muscular, club-wielding, loincloth-wearing protohuman who nonetheless invents Sufficiently Advanced technology and was the scientific rival of Mad Scientist Dr. Sivana.
Another Golden Age Captain Marvel villain was a criminal who went to prison for over 70 years and spent the entire time reading and working out until he was the smartest, most physically capable 100-year old man around.
Captain Marvel's main rival, Black Adam, also fits this trope. He has as much physical power as Superman (he practically beat the entire Justice Society on his own), but he's also superhumanly intelligent.
Really, the Big Red Cheese himself qualifies — "Wisdom of Solomon" and all that.
Victor 'Cyborg' Stone of the Teen Titans started out a downplayed version in his backstory, having an I.Q. of 196 but focusing on his athletic prospects rather than following in the footsteps of his top-tier scientist parents. After his father put him back together following the lab accident that ate his mother and much of him, he came to make a virtue of of necessity and expand his expertise in cybernetics to well-reputed authority levels by studying his own Artificial Limbs.
Darkseid. He's one of the few villains who can take on Superman in a fight and is also a brillianttactician who constantly manipulates everyone around him into getting him what he wants.
Deathstroke is basically Batman if he became a mercenary Super-Soldier and used lethal force. This means that he is both one of the best fighters in the DC Universe, as well as extremely intelligent and Crazy-Prepared.
Kilowog of the Green Lantern Corps is another one. He's one of the biggest Corps members, always fighting up close and personal and calling people "poozers", but he's also so smart that he designed the Rocket Red battle suits for the Soviet army.
The Justice League of America villain Prometheus, a Gadgeteer Genius who invented a helmet that allows him to download knowledge, including martial arts training, directly into his brain. He's one of a handful of individuals in the entire multiverse who have beaten Batman in hand-to-hand combat.
The Golden Age Hourman, career superhero and founding member of the Justice Society of America. He's a genius Chemist who created Miraclo, the chemical he uses to achieve his godly strength, speed, agility and endurance for one hour at a time. He's also an extremely successful businessman.
The Golden Age Atom was typically depicted as a short-tempered Pint-Sized Powerhouse who met problems head-on... yet he's a PhD-holding Physics College Professor who is officially listed as possessing Genius-level intellect. Originally, he was as strong as humanly possible, patterned after a Circus Strongman. Later he gained superpowers, being able to bench press the weight of an entire train, survive a nuclear detonation point-blank and flatten Tanks with just one of his patented Atomic Punches.
Lobo is rather dumb most of the time, but he is a genius when it comes to doing anything that can cause destruction. For example, he can't cure a deadly disease, but he did create a horde of mutant insects that acted as carriers for one and the vaccine for it (that's why he's the last Czarnian: he killed them all that way, with the vaccine created to make sure he survived). And he's strong enough to hold his own against Superman.
In the Metal Men's feature in Bizarro Comics, the originally incredibly unintelligent Lead is quite loquacious. Also, Doc Magnus organizes a mission just to build his creations' confidence.
Monsieur Mallah, the second of four of DC's resident mad scientist gorillas to appear on this page, and a recurring foe for the Doom Patrol.
Superboy has shown to possess superior intellect to what humans could ever have. His mind works with incredible speeds, and combined with his TTK-powers, it might be one of his greatest assets.
Supergirl: One of the most powerful heroes of the DC universe, her official power list includes "Genius-Level Intellect". And in fact she's considered a genius by Kryptonian standards, and is daughter of one of the best scientists of Krypton.
Superman himself. He is one of Earth's most powerful heroes, but he is also a master in the use of Kryptonian technology, which is far more advanced than Earth technology. He can learn at a faster rate than humans. He is the son of Krypton's finest scientist, so the scientific skills must be a family trait.
Eidetic memory and super intelligence are considered part of his power set (Depending on the Writer). Modern interpretations have the habit to make him somewhat of a Dumb Muscle to contrast Batman or other smart guys, like in Justice League: Doom:
Superman: Maybe I could move the Earth out of the way. Batman: If I had a week, I could list all the reasons why that wouldn't work.
Then there are the times villains assume Superman is just a big dumb Flying Brick, like Lex Luthor and The Joker. It always bites them in the ass. (Well, unless there's a Writer on Board.)
All-Star Superman is probably the definitive modern example of this for him. On top of his Fortress being laden with technology he's suggested to have invented himself (or at least figured out), he's also able to keep up in conversation with superscientists like Lex Luthor and Leo Quintum, and he resolves dozens of problems over the run of the comic (including most of the ones considered to be his Twelve Labors) through the use of science or guile rather than his strength.
Clark Kent is also a Pulitzer prize winning investigative journalist and a best selling fiction author.
In most depictions, General Zod is visibly larger than Superman, and doesn't pull his punches. He's also Superman's tactical superior pretty much across the board, and at least as cunning in the use of his powers as Superman himself. Notably, Zod's also Superman's big exception to Superman's code against killing, since letting Zod run loose risks the lives of millions.
Mongul has the general distinction of being one of Superman's villains who has the refined manners of a cultured gentleman and someone who's capable of running the technologically advanced Warworld, but is also a powerhouse who can exchange blows with the Man of Steel.
The Ultrahumanite, DC's first resident mad scientist, who eventually transferred consciousness into that of a large muscular gorilla, was originally written to be Superman's arch-enemy.
Diana herself, (mostly in the Post-Crisis continuity) is a Genius Bruiser. In addition to having god-like strength and unrivalled combat skill, Wonder Woman is exceptionally intelligent, being gifted at: diplomacy, multilingualism, equestrianism (horse riding), piloting, and weapons handling. Diana’s career in her civilian alter ego has also included professions such as military intelligence officer, astronaut, antiquities dealer, army nurse, businesswoman, and even secretary.
The Golden Age Giganta may have started out as Dumb Muscle, given she was just a particularly angry and violent gorilla, but after Dr. Zool put her through his Evolution Machine she became a very large, Super Strong woman who swiftly became more adapt at using the hapless Dr. Zool's genius inventions than he. The rage that had made her dangerous as a gorilla only became more pronounced and sophisticated as a "human", making her incredibly dangerous.
The Post-Crisis Giganta was a dying Mad Scientist who discovered a way to transfer her consciousness into anothers body whose assistant transferred her into a gorilla to save her life. She later transferred herself into the body of a size shifting metahuman, though she would have a more difficult time thinking logically the larger she grew and at her larger sizes was more Dumb Muscle than genius.
and peak human martial artists. Among them Barbara and Tim are considered the smartest though are no less strong being able to take on the residents of Apokolips and come back alive. Jason and Cassandra are considered the physically strongest (the former thanks to Venom) but are also keenly intelligent. Dick Grayson being the first sidekick takes after his adoptee mentor the most so therefore has the best balance of brains and brawn.