For quite a considerable stretch of time in the Star Wars timeline, Darth Vader has served as the apex predator of the galaxy. Sure, Darth Sidious/Emperor Palpatine is above him, but most of the time, Vader has been viewed as the face of the Galactic Empire and its point man where he simply directs his lightsaber towards a planet and people die.
Suffice to say, Darth Vader was a scary figure in the Galactic Empire. Still, even boogeymen have their own nightmares and Darth Vader was never immune from the fear of death nor insulated from the shame of defeat. In fact, a handful of foes have managed to nearly kill or beat him in combat.
Luke Skywalker
The most obvious victor against Vader is none other than his son who did come close to killing his own father in fair combat. Luke was no doubt one of the most accomplished Jedi in the Star Wars films considering all the handicaps he went through in his training.
Moreover, his victory served as a new starting point for the Jedi Order. In any case, the short span of time Luke took to become a Jedi is truly astounding and he was bound to become one of the most powerful Force-users in existence thanks to his surname.
Darth Sidious
One also can't discount the fact that it was still Darth Vader himself who put an end to the Galactic Empire and the current Sith menace (up until The Rise Of Skywalker). Vader managed to overthrow Sheev Palpatine both figuratively and literally (down an electrified chute).
Luke might have been there but he probably couldn't have defeated Darth Sidious on his own. In the end, Vader managed to fulfill the prophecy tied to him. As for Darth Sidious, he's by far the most dangerous enemy Vader has had. Becoming emperor of the galaxy and crushing most of the Jedi was proof enough.
Obi-Wan Kenobi
As soon as Anakin Skywalker became Darth Vader, he already faced his most persistent nemesis and lost, namely his own master, Obi-Wan Kenobi. Their first battle took place on Mustafar and Vader nearly ran out of limbs in a rather humiliating defeat.
They would only get a rematch several years later when Obi-Wan was well past his prime and that time, Vader won. Still, the fact that Kenobi could have ended Vader back in their first fight is a testament to his skill and reputation as a Jedi Master.
Galen Marek
Galen Marek, also known as Starkiller is practically a reverse Darth Vader that isn't considered canon thanks to some changes. He was raised in the hands of the Sith and was being groomed to become as good as Vader. However, he saw the light and eventually defected to the Rebellion and fought against his master.
Being raised to become a secret apprentice of Vader himself, Galen Marek became quite a handful for his master. Starkiller was one of the few people who actually became more powerful than Vader and he came close to ending him.
Kirak Infil'A
After Darth Vader got an extreme makeover with new limbs and his signature look in the movies, he was still without a lightsaber. Obi-Wan took his weapon after their battle. Darth Sidious instructed Vader that Sith lightsabers can only exist if a Sith corrupts another Jedi's lightsaber. That meant Vader had to hunt one down.
It just so happens that an isolated Jedi named Kirak Infil'A was available. At first, Kirak won against Vader and even threw the Sith Lord off a cliff. Vader, however, really needed the lightsaber and went for a rematch until he won.
Stauz Czycz
Thought Luke Skywalker was impressive as Vader's enemy? Then perhaps Stuaz Czycz might disagree. He's one of the victims of the Galactic Empire's planetary purge and personally witnessed Vader slaughter his own family. Stauz was initially but a mere skinny and small alien soldier.
But through sheer determination and lust for revenge, Stauz spliced himself with enough cybernetics to become nearly unrecognizable from his original form. Afterward, he worked up to become one of the top bounty hunters for the Empire until Vader considered his service. Stauz attacked Vader during their personal talk and also nearly defeated the Sith Lord but both of them froze upon peering into each other's hatred-filled mind. Vader managed to snap out first and finish Stauz.
Ahsoka Tano
Apart from Starkiller (though he's non-canon) another apprentice that would later challenge Vader is Ahsoka Tano, a veteran of the Clone Wars and one of Anakin Skywalker's closest friends. She was a gifted Jedi but was left of the Order after some false accusations.
Since then, she worked as an independent warrior of the light side and served secretly under the Rebel Alliance. Eventually, she crossed blades with Vader and the two of them fought to the death. Vader nearly won but Ahsoka managed to survive thanks to a friendly and mystical intervention.
Morit Astarte
Morit Astarte was a clone created by an accomplished doctor who was commissioned by Emperor Palpatine himself. Along with others, Morit was to be a replacement for Vader and was engineered to be as good as him. Vader discovered the existence of these genetically-engineered children and fought them in a free-for-all at the Emperor's behest.
Vader was nearly defeated by several of the replacements until Morti stepped in to save him. It's safe to say that without Morit, Vader would have long perished. By no means does that imply Morit was an ally to Vader and the two have also fought for the Emperor's favor.
Celeste Morne
Celeste Morne only existed in the Legends and not the canon part of Star Wars lore much like Starkiller. However, she's definitely one of the most exceptional enemies Vader has fought regardless of his version. Celeste Morne was an ancient Jedi who was possessed by a Sith Lord.
Celeste could turn people into rakghouls and she used this to her advantage when fighting against Vader and his lackeys. Celeste was even able to force Vader to retreat, something not many Force-users can claim to have done.
Grand Moff Tarkin
By far the most impressive person to have defeated Vader was his own ally, namely Grand Moff Tarkin. Ever wondered how Tarkin could easily order Vader to stop doing something? That's because both of them had a duel to prove that even someone like Vader wasn't invincible.
Tarkin used his cunning and ruthlessness to lure Vader into a spot that attracted lightning and the latter was struck down with his circuitry and robotic parts fried. After this, Vader came to respect Tarkin more so than before.