A while ago I answered the question whether "great warriors" really existed (the answer is no). However, your question is a little different, so I'll rephrase the answer. Yes, "legendary warriors" existed; but also yes, the variance in fighting capabilities among ancient fighters was much much smaller than is conveyed in culture and myth. The key to this paradox is that the bar for the status of legendary warrior is much, much lower than pop culture would have you believe.
Fundamentally, skill at arms was not a significant factor in premodern warfare. My area of expertise is ancient Greece; in that culture, no one particularly cared whether you were good at using a spear or sword, and no battle was ever won because one side had more technically proficient fighters than the other. The Greeks made fun of people who professed to be skilled spear-fighters or swordsmen, thinking that these people had mastered a useless skill and were bound to make fools of themselves in actual combat. It wasn't until after the conquest of Greece by Macedon that armed fighting came to be widely taught as part of a civic upbringing. What mattered, instead, was the willingness to fight. As long as you were brave - as long as you were prepared to stand your ground and "look spears in the face" - you were already doing enough. Morale was decisive; weapon proficiency was comparatively trivial.
The main distinction between Greek warriors, then, was not their fighting ability, but their readiness to face hardship and danger. As the Spartan poet Tyrtaios put it:
This is a common benefit for the state and all the people: when a man stands firm in the front without ceasing, and, making his heart and soul endure, banishes all thought of shameful flight, encouraging his neighbour with words. This is a man good in war; he quickly turns the waves of enemy spears, and stems the tide of battle with his will.
A good warrior is not one who kills many, or who outmatches his enemies in skill. A good warrior endures in the heat of battle. A good warrior encourages others to endure. The difference between a good warrior and a bad one, then, is the amount of time he is prepared to stand in the front rank before he turns to flee.
Admittedly, in the Iliad - the ultimate account of ancient Greek heroic ideals - the Greek heroes are explicitly ranked by their skill: Akhilleus is the best of the Greeks, then Aias son of Telamon, then other heroes like Diomedes, Odysseus and Agamemnon. But the striking fact about this ranking is that it doesn't affect the way their actions are described in combat. Most fights in the Iliad are over in a single blow; there are no extended sword duels or spear fights at all. Every hero is able to dispatch enemies in droves. The first great accounts of such carnage that we get in the poem are the killing sprees of Agamemnon and Diomedes (who ends up wounding both Aphrodite and Ares). The only difference between a hero like Sarpedon and the great Akhilleus is that someone eventually stops him. Heroes survive through luck, strength, armour, and the favour of the gods. Homer does not appear to have any way of describing how one hero might be better at fighting than another. Indeed, there is no reference to combat training anywhere in the epics, and most of what the heroes do in combat seems to have been learned from hunting and active warfare.
The real difference, and the thing Agamemnon and Nestor actively seek to secure in their men, is the willingness to move to the front and stay there. People like Aias are described as "towers" - they never move, do not retreat in the face of danger, and allow others to rally around them. Heroes like Odysseus and Akhilleus surge forward and force the enemy back. In other words, the ideal hero is not someone who can best his opponent in a swordfight, but someone who shows courage and inspires courage in others. In Homer's idealised battlefields, but also in reality, this was the truly decisive factor.
We see this clearly when we turn to the legendary warriors of actual history. Authors like Herodotos and Plutarch like to commemorate heroic behaviour; they are interested in preserving worthy examples and awe-inspiring stories. But the heroes they record are always heroically brave, never heroically skilled. These men don't get a kill count; their stories are like that of the Athenian Sophanes, who anchored himself to the ground and challenged his enemies to come at him, or that of the Spartan Isidas, who went into battle for his hometown straight from the gymnasium and fought naked. Sokrates himself was a famous warrior, not for his skill with the spear, but because he kept a cool head even in defeat:
"I noticed, first, how far he outdid Laches in collectedness, and next I felt—to use a phrase of yours, Aristophanes—how there he stepped along, as his wont is in our streets, 'strutting like a proud marsh-goose, with ever a side-long glance,' turning a calm sidelong look on friend and foe alike, and convincing anyone even from afar that whoever cares to touch this person will find he can put up a stout enough defence. The result was that both he and his comrade got away unscathed: for, as a rule, people who act this way in war will not be touched."
-- Plato, Symposion 221
In short, there absolutely were real human beings who were renowned for their worth in a fight. However, that worth was not determined by their skill with spear or sword. It didn't really matter how many enemies they killed, or whether they even killed any. A legendary warrior was one who had proven himself brave when it mattered; someone who could serve as an example to others, who also needed to be brave. Facing such a man in battle would be terrifying. Fighting alongside them would be inspiring. The actual difference in ability between these warriors and the men beside them in the line would be negligible. Nevertheless, some of their names have been recorded as worthy of note, and have survived for thousands of years, because they overcame their fear when it mattered.
Can someone specifically comment on the Japanese concept of kensai or a sword saint? Shinmen Munisai, Miyamoto Musashi, and Miyamoto Iori constitute a lineage of legendary warriors. Clearly they were accomplished duelists, but are there any accounts of individually lionized warriors having an outsized effect on the actual battlefield?
Coming at this from a different perspective from the excellent answer from u/Iphikrates, Three Kingdoms China (190 C.E to 280) which will hopefully be of use to u/crusaderblings2. In many ways, this bit of Iphikrates answer
Yes, "legendary warriors" existed; but also yes, the variance in fighting capabilities among ancient fighters was much much smaller than is conveyed in culture and myth. The key to this paradox is that the bar for the status of legendary warrior is much, much lower than pop culture would have you believe."
remains the same with mine despite the differences in terms of warrior skills
So part of the way armies of the era fought involved warriors, particularly during the times of raised local troops and family retainers but even when there was stronger central administration, warriors like Wei Yan were valuable. When you have an army of limited coordination with soldiers who might not want to be there and not always be well equipped, anyone experienced like Sun Jian or Qu Yi from before the war was valuable. Those who had spent the preceding years carrying out acts of violence as errants like Dian Wei could also be useful. Warriors with their hand-picked and hopefully well-equipped "Companions" acting as line breakers, trying to punch a hole in the enemy lines. Ideally inspiring one's soldiers and hopefully putting fear in the other side. Or, when things went horribly wrong, to bravely stand and get their lord away at the cost of wounds, the lives of their friends and possibly even their own.
Such men with the confidence to put their bodies on the lines time after time despite the risks were not always helpfully subservient. Or well behaved. Ego's in an army could bristle leading to commanders or coordinating officers having to try to prevent it from being disruptive. Sometimes an execution would have to be ordered for fear the warrior was getting out of control (Qu Yi), sometimes the ego exploded into doing something incredibly stupid (Wei Yan's mutiny), an army could be hampered by the infighting from the ego's of officers. Orders might not be obeyed (Zhou Tai struggling to impose himself at Ruxu) or an officer attempt to do something by themselves (Cao Xiu). The retainers of the warrior might not be kept under control (Cao Hong and Lu Bu), the warrior might commit murder (Zhu Huan and Pan Zhang perhaps two of the more violent warriors of the era).
A warlord's ability to keep such men from killing each other, loyal and coordinated was a test of personality and each had to decide where they might draw the line. Both Yuan warlords Yuan Shao and rival Yuan Shu would reject Lu Bu due to his arrogance and limited control of his men leading to excessive pillaging. On the other hand, the southern warlord turned Emperor Sun Quan, a brave and reckless warrior and dealing with his warriors having personal commands, would turn a repeated blind eye to literal murder.
Of course, not just warriors the warlords and Emperors had to try to keep focused and egos in check and warriors could be looked down by scholars as mere fighting men. Warriors could be a handful but they were kept around because they were needed.
Some better than others?
Where some were more able than others as warriors and recognized as such? Yes.
Unsurprisingly perhaps, you have a lot of people doing something and some will excel at it. Being strong and brave was one thing, plenty could be found that fit that description, but some were noted as exceptionally strong or brave, some excelled with archery or weapons. Moments were put in the record to celebrate their strength or comparisons made with heroes of old and held up for contemporaries to be compared to.
Like Dian Wei the head of Cao Cao's bodyguards and champion eater. He was supposed to have wielded an approximately 20-kilo weapon and once put up a headquarters banner one-handed when nobody else under Major Zhao Chong could do so with two. Cao Cao's commanders Cao Ren (a kinsman) and Zhang Liao were seen by the later scholar Fu Xuan as the two bravest men in Wei ranks and both of them were credited with leading raids into invading Wu ranks (Zhou Yu at Jiangling, Sun Quan at Hefei) then dashing back into the fight to rescue men left behind. Shu-Han officer Zhao Yun's valour was compared to past warriors of the Han by Chen Shou, the writer of the records, and other figures within Shu-Han like Chen Dao were compared to him.
You also had rare examples of where the bravery in battle caught the attention of others beyond their own faction and beyond "well this is a brave figure"
Lu Bu, the perhaps most famed example of a warrior in that era, for all his flaws as a commander, officer and warlord: He was very strong but it was more than that, he was an expert with bow and horse, agile (which proved helpful when Dong Zhuo threw weapons at him). He won a duel against Guo Si in the failed defence of Chang'an, used his archery in a bet to force peace (his arrival with fresh troops were perhaps more of use in persuading Ji Ling to withdraw). His skill in battle earned him nicknames and stopped Yuan Shao's officers from pursuing him when he fled from Yuan Shao's attempt to assassinate him. For all the disparaging comments from Cao Cao's camp, they acknowledged his ferocity in battle that was compared to the famed warrior and warlord Xiang Yu made him a potential threat if the circumstances were right.
Guan Yu and Zhang Fei, warriors and close companions to the sandal maker turned commander turned Emperor Liu Bei, were seen as worth ten thousand men by Cao Cao's adviser Cheng Yu. Sun Quan's commander Zhou Yu wanted to isolate Liu Bei in a golden cage and hire them both to be part of his army. Zhang Fei was an intelligent commander but we get few examples of his strength due to poor records of Shu-Han, we more note his violence and brutality towards his own men which would eventually get him killed. Guan Yu was seen as Zhang Fei's superior as a warrior, the man with the famed beard and sense of honour was noted to have ridden into the midst of an army to slay the Yuan Shao commander Yan Liang and fight his way back out. He was admired by Cao Cao and seen by various commanders of Sun Quan as a threat despite what seems (from the limited records we have) to have been a rather spotty military record as a general.
Nobody considered such warriors unstoppable, even the ones that drew admiring or fearful glances elsewhere. Lu Bu might have been an impressive warrior but he lost many a battle, he was unreliable, left him politically isolated via his erratic behaviour, lost support of his men and before then couldn't effectively command and coordinate them, couldn't trust his officers when push came to shove (not without reason) to be left alone. Lu Meng dealt with the Guan Yu danger by playing on his ego while Guan Yu falling out with some senior officers cost him dearly, Zhang Fei's brutality cost Liu Bei his first base in Xu (Liu Bei never left him in charge of anywhere so key after that), raised concerns from Liu Bei and eventually Zhang Fei was killed by his abused men. Being mighty helped at some level in the war but other things were needed and such mighty men did sometimes have big flaws that helped lead to their fates (the Romance loved to play on this).
Part 1 of two
There's an excellent answer here for the Hellenistic world, but as someone who grew up playing Dynasty Warriors and has read just about every tale of ancient Chinese wars, China has dozens if not hundreds of legendary warriors.
Does that reverence match their warfare style? How does it differ from the Greek style?