The Arrowverse is packed with over a dozen skilled fighters, with the greatest of them all being Ra’s al Ghul (Matt Nable). Ra’s al Ghul is primarily known in the comics as the character who trained Batman, but he appeared as the main villain in Arrow season 3 - just one of many ways the Arrowverse had incorporated Batman's universe without using the Dark Knight.
Though Ra’s al Ghul is an important part of Batman’s corner of the DC Universe, he was set up to join Green Arrow’s show in season 2 when the League of Assassins was first mentioned. In the show’s third season, the group became a real threat when Malcolm Merlyn (John Barrowman) used hypnotism to make Thea (Willa Holland) kill Sara Lance (Caity Lotz). Since she was a League member, this caused the organization to take action. What followed was a showdown between Oliver and their leader, Ra’s al Ghul. Oliver lost, but the fact that he survived was enough to convince Ra’s that Oliver deserved to be his successor. But at the end of the season, Oliver was forced to kill him.
Ra’s al Ghul was by far the Arrowverse’s most seasoned warrior. It makes sense that he would hold this title, considering that he’s been around for centuries, thanks to the Lazarus Pit. The vast number of martial arts styles that Ra’s demonstrates in season 3 shows that he has taken full of advantage of his extended longevity by taking the time to constantly improve his fighting skills. Oliver has had multiple teachers training him over the years - including Ra’s al Ghul himself - but despite the diverse background he has in martial arts, his experiences can’t compare to someone who has been making himself better for hundreds of years.
The Arrowverse provided a good indication of just how good Ra’s al Ghul is when he battled Oliver for the first time. Oliver, who at the time was on par with characters like Deathstroke (Manu Bennett) and Malcolm, was easily bested by Ra’s in sword-fighting. No non-superpowered character has ever put Oliver to shame as effortlessly as Ra’s did in that episode. Oliver did end up killing him in the end, but that’s only because he was able to catch Ra’s off-guard. He never did manage to beat him in a fair fight.
It’s important to keep in mind that the skills of several of the Arrowverse’s best fighters originated from Ra’s al Ghul. Many were either trained by him directly or by one of his people with the League of Assassins. Since they can only have a small portion of his knowledge of fighting, they wouldn’t be able to rival him in combat. His skills put him far above those of all other Arrowverse heroes and villains. The evidence for that is that Oliver, at one point or another, has beaten most of the Arrowverse’s most skilled combatants, including White Canary, Prometheus (Josh Segarra), Malcolm, Deathstroke, and Damien Darhk (Neal McDonough). All things considered, Ra’s al Ghul is without a doubt the Arrowverse’s best fighter, with the Emerald Archer taking second place.