The duel. Darth Vader defeats Darth Maul. The two Sith Lords engaged in a lightsaber duel, going through the volcano and onto a bridge situated over a river of lava, which collapsed, though they both survived and continued their battle.
Yep. Darth Maul didn't really say or show straight up that he "feared" Darth Vader, but he openly stated his belief that he could not defeat Darth Vader without the help of the Jedi, therefore on his own.
Darth Maul knew that Anakin Skywalker was the so-called Chosen One, and that he had been groomed by Darth Sidious to become his new apprentice, Darth Vader.
Although they didn't interact with each other, Anakin Skywalker first met Darth Maul on Tatooine during the events of The Phantom Menace and then later on in the film on Naboo.
Darth Maul became apprenticed to Darth Sidious while still a child. Darth Tyranus and Darth Vader, both former members of the Jedi Order, became Sidious' apprentice, in turn, as adults.
Considering his infamy, it's hard to deny that Darth Vader is the more powerful of the two, but his victory over Maul wouldn't come easily. As the Emperor's enforcer, Vader is terrifying.
This information comes to light form the comic series Darth Vader: Dark Lord of the Sith by Charles Soule and Giuseppe Camuncoli, in particular issue #7. Palpatine admits to Darth Vader that the Jedi he actually feared most was none other than Jocasta Nu.
Appealing to the hate and conflict within him, Darth Sidious goaded Luke into attacking. Vader defended the Emperor and he and Luke were locked in mortal combat. Luke lost control of his anger, viciously attacking Vader, finally beating him down and chopping off his hand with his lightsaber.
During the Imperial Era, a human female nurse served the Galactic Empire on board the Death Star under the supervision of a doctor. They both served the Sith Lord Darth Vader as his personal medical caretakers. The nurse became obsessed and psychotically in love with the Dark Lord of the Sith.
DARK SIDE FRIDAY - Did you know Palpatine feared Qui-Gon Jinn? Palpatine was immensely powerful and he could see the future which made him very confident about pretty much anyone who stood against him.
In the film's climax, Maul duels Qui-Gon and his apprentice Obi-Wan Kenobi (Ewan McGregor). He is able to kill Qui-Gon and knock Obi-Wan down a shaft, but Kenobi propels himself out of the pit and uses Qui-Gon's lightsaber to bisect Maul, sending the two parts of his body falling down the shaft.
The battle
Maul was tracked to Zanbar by General Grievous, the leader of the Separatist military, and a Separatist fleet. Dooku ordered Grievous not to kill Maul, simply to defeat and wound his forces enough that Maul would seek out Mother Talzin's help.
Throughout this time, Maul dueled Obi-Wan Kenobi on numerous occasions, and in an act of pure hatred, killed Obi-Wan's former love, Duchess Satine Kryze. His revenge would prove double-edged, however, as the act created a dark side ripple sensed by his former Master, Darth Sidious.
It appeared that Darth Vader was more machine than we thought. His armor could be hacked and controlled by a device. In a turn of events, Darth Vader's right limb holding his dangerous scarlet lightsaber was moving of its own accord toward his neck. This was a dangerous weakness indeed.
Admiral Ozzel : [appearing onscreen with Captain Piett] Lord Vader, the fleet has moved out of lightspeed and we're preparing to... Darth Vader : You have failed me for the last time, Admiral! Captain Piett?
The Jedi Didn't Save Grogu, Vader Spared Him.
1/15 Luke Skywalker
Having faced his father once before, Luke was familiar with his tactics and used the force to gain an upper-hand. In Star Wars Canon, only Luke Skywalker can be acknowledged as the one who truly defeated Darth Vader.
The ever stronger fear
In the Phantom Menace, Master Yoda senses much fear in Anakin, however, this fear is not the understandable anxiety - Anakin is afraid to lose his mother, Shmi, whom he was forced to leave behind in slavery.
Visions of Obi-Wan. The comic opens during the last moments of Revenge of the Sith, recreating the well-memed instance when a despondent, freshly-armored Vader cries out with a drawling “nooooooo” over how much he's lost.
By the time of Episode 3; Anakin is in his prime, and already one of the Jedi Order's most powerful “masters” (although technically still a knight), just behind Obi-Wan, Windu, and Yoda. Maul wouldn't stand a chance. Anakin stomps.
Due to his proficient skills within the force, Yoda is also an incredibly skilled lightsaber combatant. He is one of the highest-ranking Jedi in the Jedi council. Because of his Force sensitivity, Yoda would easily be able to evade Maul's attacks.
Even in the old Star Wars canon, the two had a confrontation, as they met in the comic book Star Wars Tales #9, where Maul pieced together that Anakin was Vader.