The heroes of the Arrowverse have faced a wide range of threats through the years and over the course of 7 shows. Some fights have required the heroes to band together to defeat their enemies, while others could be accomplished alone.
Whether human, alien, or demon, essentially all Arrowverse fights come down to who is stronger. Intelligence can also be important, but it is definitely not the deciding factor in battles. Powers can certainly give both heroes and villains an advantage in combat, but their real skill is best measured in fighting techniques and experience.
Lex Luthor
Played by several actors over the years, Lex Luthor is a prominent recurring villain in both Superman mythology and the Supergirl series; he was also an important part of the "Crisis on Infinite Earths" Arrowverse crossover. Lex is known for his incredible intelligence, extravagant schemes, and unrelenting hate for Kryptonians. However, though he often proves to be a formidable foe intellectually, he does not have many natural combat abilities.
He has historically relied on his technologies like the "Lexosuit" and Kryptonite weapons when fighting with Superman or Supergirl. The Kryptonite weakens his opponents so that he can use the strength of his suit to fight them, making up for the fact that they are more skilled fighters.
Eva McCulloch
Eva McCulloch, also known as Mirror Mistress, was the major villain for the second half of The Flash's sixth season and the beginning of its seventh. An interesting thing about Eva's fighting technique was the fact that she fought a psychological battle with Team Flash and Central City by replacing various people from the heroes' lives with mirror duplicates and holding the originals captive.
Mirror Mistress' fighting skills were entirely tied to her powers, but she managed to get the upper hand on Barry Allen in a way that few villains are able to due to her decreasing his speed. Eva repeatedly hit Barry with her mirror shards and could have easily killed him if she wanted to. Even after he regained his powers, it took the combined efforts of Team Flash to beat the Mirror Mistress and her duplicates.
Tobias Whale
Tobias Whale was the main antagonist to Jefferson Pierce for all 4 seasons of Black Lightning. Tobias was both a smart and cunning adversary, who seemed to get the upper hand due to the decisions he made. He was also a trained martial artist. Though viewers did not often get to see him personally fight his opponents, in season 1 he easily defeats a fighter who had taken the physically enhancing drug "Green Light."
Until the series' finale, Tobias was shown to be essentially ageless, meaning he remained in peak physical condition despite being in his seventies. Jefferson Pierce possessed superior skills in hand-to-hand combat, but Tobias' enhanced strength made them more evenly matched when fighting. Without his powers, Jefferson was easily bested and nearly killed by Tobias.
Eobard Thawne
The Reverse-Flash is Barry Allen's sworn enemy, but he was also his former mentor and thereby taught Barry a lot of what he knows when it comes to fighting as a speedster. For a long time, the Reverse-Flash was better able to utilize his speed when making attacks than Barry was.
When Barry faced Thawne in the season 1 finale, he needed both Oliver Queen and Firestorm to help subdue him. The Reverse Flash's experience and intelligence as one of the Arrowverse's smartest villains both contribute to his technique, so that even though Barry continually gets faster, Eobard Thawne continues to manage to beat him by making smarter attacks.
Slade Wilson
While Slade Wilson may not be the most powerful villain, he is certainly one of the most skilled fighters. Even before being dosed with Mirakuru super serum, Slade Wilson was a trained assassin and member of the Australian Secret Intelligence Service who went by the code name "Deathstroke."
Slade's expertise in combat was augmented by the superhuman strength, healing, reflexes, and agility he got from the Mirakuru serum. Oliver Queen's skill is a testament to Slade Wilson's fighting ability as he taught Oliver a significant portion of what he knew about fighting.
Reign (Samantha Arias)
Reign, the alternate personality of Samantha Arias, was one of three Kryptonian world-killers that plagued Supergirl during season 3. Due to being genetically enhanced, Reign is physically stronger than all other previously encountered Kryptonians on the show. During Supergirl and Reign's first fight, Kara struggled to even get a punch in, even though she fought without reservations.
Reign possessed all the abilities of a typical Kryptonian and then some. After the other two world-killers died, she also absorbed their powers. One problem with Reign, however, was that she relied on brute force and powers more than skill; take away her abilities and her fighting skills were a bit lacking.
Damien Darhk
While he often relied on his magic in combat, Damien Darhk was a trained member of the League of Assassins. At one point, he almost became the next Ra's al Ghul. One of Damien's tricks involved immobilizing his opponents so they were powerless against his attack. It was by this means that he killed the original Laurel Lance.
Damien Darhk's arc on Arrow was a bit disappointing overall as he was defeated surprisingly easily in the end by Oliver Queen, but he proved to be a far more formidable foe for the Legends of Tomorrow. After he was resurrected, his magical abilities became even stronger. The Legends only defeated him because he decided to work with them to save his daughter, Nora, from the demon Mallus.
Mallus
As a time demon, Mallus had a unique skill set that he used to torment the Legends. He possessed multiple members of the team, imbuing them with his abilities in addition to their own skills. During their final showdown, he displaced three armies to fight the Legends in the town of Salvation, North Dakota. Mallus could fly, throw fire, and resurrect the dead, to name a few of his powers.
Fighting Mallus required the combined abilities of six of the Legends wearing the totems of Zambesi, plus the others who had to fight off his forces. The release of Mallus allowed many other demons to also escape their prisons, so the time demon's realm continued to cause havoc for the Legends even after Mallus was defeated.
Dominators
The Dominators were the first villains the heroes of the Arrowverse faced in a full-scale crossover event. The Dominators were intelligent, incredibly strong, and nearly invulnerable - even to heat vision, in addition to being skilled in battle tactics and hand-to-hand combat.
Their advanced technology and mental abilities allowed them to capture and manipulate the heroes while planning to destroy Earth's metahuman population. It required the combined efforts of the Arrowverse to rid the planet of them. The Dominators eventually retreated, but they have later appeared in smaller numbers as a continuing threat to the planet.
The Fates
The Fates did not often personally fight the Legends, unlike many other villains who challenged them, but they used Astra's abilities to resurrect "encores" to fight the team for them. Once the Fates were in possession of the Loom of Fate, they had the ability to rewrite the whole of reality and remove free will. Without the Loom, Lachesis' powers consisted mainly of magic, but she was also able to manipulate others into doing her bidding. Atropos was the most skilled fighter of the three Fates.
Even without her full godly abilities, Atropos was able to beat Sara Lance, a trained assassin, and murder many other people in searching for her sister and the Legends. She was a master martial artist and knife-wielder, in addition to her godly strength and durability. While the Legends and the other Arrowverse heroes have fought many dangerous creatures, literal goddesses have to be contenders for the most powerful fighters.