When it comes to champions that top the charts in the 1v1 category, it's important to differentiate between the different types of champions because some categories counter others in a 1v1. The main categories to discuss are juggernauts, tanks, assassins, mages, marksmen, and duelists. Let's look at each:

Juggernauts

Juggernauts are bulky and can dish out a lot of damage. The only problem is they are generally immobile and are quite weak to kiting. As you might expect, they are therefore weak to marksmen when on even footing. On even footing, they are much better against tanks because they can tank damage for nearly just as long, but dish out much more. To beat out marksmen, juggernauts must keep in mind that they need to get on top of the enemy if they want any chance to win. So, juggernauts should look to ambush the marksmen and keep whatever form of gap-close they have for when the marksmen start kiting or escaping. With that said, here's the best of the category:

Aatrox

Aatrox has a fun kit with a lot of damage and low cooldowns. Although his kit is quite difficult to get comfortable with, when mastered, his naturally bulkiness and sustain will allow Aatrox to just outlast enemies in the 1v1 and eventually win.

Darius

Darius' bleed and true damage make him very difficult to beat in an extended fight. If Darius can get on top of his enemies and stay there, it's pretty much lights out for the enemy.

Garen

Garen's versatile build paths for higher damage or bulkier presence, make him very effective at building to counter the enemy. Either way, Garen's damage and bulkiness will still be quite apparent. Like Darius, it's just a matter of getting on top of the enemy if you want to win the 1v1.

Sett

Sett's versatile kit provides him with a shield, true damage, auto-attack resets, and crowd-control. He can almost be considered an easier (and arguably better) version of Aatrox. Sett is incredibly useful in fights but can do just as much work in the side lanes winning 1v1s.

Trundle

Perhaps a surprise to see on this list, Trundle is very underrated in his ability to win 1v1s. Trundle is perfect to beat out tanks because of his Ultimate ability, but also has insane damage numbers and steroids that he gets from his Q and W abilities. Not only that, he has some outplaying potential with his pillar to cancel channeling of abilities, or at the very least help lock down targets that are trying to maneuver around him in a 1v1.

Tanks

Tanks, on the other hand, are tankier (obviously), but deal less damage. To make up for it, they have a better time getting onto targets and locking them down. The issue with tanks is they don't have the prolonged damage to beat out juggernauts. Where tanks do excel in the 1v1 is against assassins and mages. On even footing, tanks easily can survive the initial burst of assassins and mages. With their burst out of the way and their abilities on cooldown, tanks have enough damage they can kill an assassin or mage so long as they stay on top of them. To better a tank's chances in a 1v1 against a juggernaut, tanks should keep an eye on juggernaut's cooldowns and try to capitalize on an opportunity when their abilities are on cooldown. Additionally, juggernauts have very straightforward abilities and usually some ability to deal with tanks, so tank players need to assess the situation well to know if there even is anyway to beat them in a 1v1. With that in mind, here's the best of the category:

Zac

Zac's ability to heal tremendous amounts of his HP while having high base stats and crowd-controlling abilities puts him in a perfect spot to make this list as one of the best tank 1v1 champions. If players make sure to pick up their blobs, they can easily out sustain others on this list.

Malphite

Malphite's insane armor stacking power makes him nearly impossible to kill for AD damaging champions. His higher-than-average base damage and stats give his abilities surprising amounts of damage that can nearly one-shot enemies.

Maokai

Maokai has such insane crowd-controlling abilities and low cooldowns that he can practically permanently keep enemies crowd-controlled. Even if he doesn't, all his abilities deal damage and will slowly take down most opponents!

Ornn

Ornn is probably the perfect example of being over tuned in his base stats. With true damage, heavy crowd-controlling abilities, and insane tankiness, there isn't really any champion that even would want to take a 1v1 against him (even if they should win) just because of how long it would take to kill him!

Sion

Sion's never-ending HP stacking and high base stats make him a force to be reckoned with. Like Ornn, it's almost not worth even attempting to 1v1 him because of the sheer amount of time it takes to kill him. Not to mention his passive when he does die, will probably end up getting you killed if he doesn't end up winning the 1v1 in the first place!

Assassins

Assassins are what most people picture when they think of 1v1ing champions. They are fantastic for their ability to gap-close onto targets and with their immense burst of damage they can get in and out in a flash. However, as you might expect, any champion that can survive the initial onslaught of damage, will have a pretty good chance to win out on the 1v1. So, the best classes to fit that bill are the tanks and juggernauts. More specifically, tanks are better into assassins that are more mobile, and juggernauts are better into less mobile assassins. It's also worth mentioning that assassins tend to be the most difficult to execute in 1v1s so there is decent outplay potential as well. With that said, here are the best of the category:

Zed

Zed's high burst damage, and outplay potential are exactly why he finds himself on this list. You can't see a 1v1 highlight montage without seeing a clip with Zed, and that's because he's just that good at them!

Kha'Zix

Kha'Zix isolated damage and invisibility makes him a true hunter. If you are alone with a Kha'Zix in the game, you always need to be looking over your shoulder!

Qiyana

Although Qiyana is still widely misunderstood, her unique playstyle and abilities make her exceptional in the 1v1 department. Her high mobility and flashiness make for a world of pain to any enemy with less than two thousand HP.

Ekko

Ekko's ultimate ability to basically rewind to attempt a 1v1 again gives him a huge edge over his opponent. With great burst, crowd control, and mobility, Ekko is a fantastic choice for side lane pressure and 1v1 prowess.

Kassadin

Kassadin's mid-to-late game scaling is insane. At level 16, his ultimate cooldown is low enough that you pretty much don't even have to use other abilities. His ultimate damage scales with stacking and provides him with gap-close to make for a huge burst of damage out of the blue.

Mages

Next are mages. Mages offer ability-based damage that can easily one-shot targets. In general, burst mages would be the subclass that will be discussed because they are better than the rest in 1v1s. The benefit of this class that separates them from traditional assassins is their ability to offer utility and crowd-controlling effects to enemies. As they are burst reliant, they like assassins, and weaker to tanks and juggernauts that can survive the initial burst. To beat out juggernauts and tanks, mages should look to keep their crowd-controlling and utility abilities to keep the enemy at bay and buy some time for the damaging cooldowns to come back up. Here are the best mages at 1v1s:

LeBlanc

LeBlanc is a champion on the border between the assassin and mage classes. She has the ability to generate insane damage numbers in a burst-like fashion when using her ultimate after the appropriate spells, but at the same time, she can use these abilities to provide more utility and crowd-controlling effects to buy some time before her other damaging abilities are back off cooldown.

Neeko

Neeko's range and surprising burst damage make her a fantastic 1v1 mage. Not only can she be deceptive with her passive and bait in enemies, but she can also use her W to go invisible to engage for an easy Ultimate or gap-closure. Not to mention her passive on her W provides her with a three-hit bonus damage on her auto-attacks which really pack a punch at the all stages of the game.

Sylas

Sylas' versatile kit is excellent for drawn out fights because of his low cooldowns and healing from his W. If Sylas can survive initial bursts of damage, Sylas can generally prolong the fight to get off several heals with his W to make the difference in the fight.

Syndra

Syndra's low cooldown on her Dark Sphere is crucial to her ability to stack up spheres to have greater damage and benefit from her other abilities. Landing even one or two Dark Spheres can easily be enough to follow up with her ultimate on a squishier target and guarantee the kill. Afterall, it isn't named the 'Gameplay Button' for nothing.

Ahri

Ahri's multi-striking abilities allow her to apply damage constantly. With true damage, crowd-controlling engage that offers extra magic damage for following abilities, and multiple casts of her ultimate for repositioning and even more follow-up damage, Ahri's 1v1 potential is very potent from even a screen away.

Marksmen

Marksmen are an excellent class because they have an immense amount of sustained damage that can easily kill any other class in this category. To make up for it, they of course, are the easiest to kill. Some marksmen do have mobility, but some do not. So, the easiest class to beat is tanks because of their high damage per second and sustain to reduce the already lackluster damage from the tanks. In general, with mobility or not, they are generally considered to be not mobile enough to escape from their countering classes. Who destroys the marksmen? Assassins, and mages. Assuming these classes have their abilities available, their high burst damage will easily beat out marksmen in a 1v1. To beat assassins and mages, the strategy is quite unique for each marksmen. Higher mobility marksmen should look to use their mobility to dodge whatever skill shot-based damage the mages and assassins have. That is the only chance marksmen must survive their burst. With that out of the way, marksmen should have enough time to kill the assassin or mage before they have the time to get their abilities back off cooldown. The other option (for less mobile marksmen), is to wait for the opportunity to initiate the 1v1 when the assassin/mage has used all, if not most, of their abilities. This essentially gives the marksmen a leg up in the 1v1 with some time to dish out free damage before their abilities come back up. Here's the best 1v1 champions of the category:

Draven

The ideal features you would look for in a marksman for 1v1s is probably what you'll find in Draven's kit. Attack damage steroids, attack speed steroids, movement speed, ability resets (in his W), some sort of crowd control, and a high damage ultimate. Draven's raw auto-attacking power when his Q is active give him more than enough damage to kill weaker enemies in only a couple of auto-attacks.

Lucian

Lucian's passive giving him two auto-attacks after each ability cast is insanely powerful for 1v1s. In combination with his already powerful 1v1 kit, a great Lucian player will weave auto-attacks between abilities to make combos smoother than butter.

Vayne

Vayne is probably the ideal champion that players think of for a list like this. Vayne's high damage from her Silver Bolts, damage steroid, speed boost, and access to invisibility from her Ultimate, Vayne probably has the easiest time dealing out enough damage to kill any target she is given even a couple of seconds to attack. And how does she get that much time to attack enemies? With a well-placed Condemn into a wall/structure, Vayne stuns her target and can freely attack her enemy to death.

Kai'Sa

Kai'Sa is in an incredible position for 1v1s, especially in the later stages of the game when she has her Q and E abilities upgraded. Her isolated Q damage when upgraded is quite high and with such a low cooldown can be cast multiple times in a 1v1. With her E providing her with invisibility and speed to reposition and dodge (not to mention the attack speed buff), Kai'Sa can shred down even the tankiest enemies on this list with her passive. With all of that said, Kai'Sa still has her Ultimate ability to dodge out on other key abilities, get a nice shield and even chase down her opponents when marked.

Xayah

Xayah may come as a surprise on this list because she is not in a great position in the meta. However, Xayah's kit gives her an attack speed steroid in her W ability, a root (with tons of damage) in her E ability, and an Ultimate ability that allows her to dodge out on key enemy abilities during the 1v1. When used correctly, a few auto attacks, along with a well-timed ultimate and E cast, she can easily burst lower HP targets.

Duelists

Finally, arguably the best category as the name suggests, duelists. Duelists aren't considered a class in League of Legends, but this category covers some champions that fit into multiple categories, but really excel in the side lanes where they can have their 1v1s all game long. These champions have several features that make them duelists. They have mobility, low cooldowns, low/no ability costs, diverse builds that allows them to adapt to games better than other classes, and are either quite bulky, or have methods of sustain to survive in fights. Some duelists are easier to play than others and are quite unique when all aspects are considered. As such, each duelist specializes against the other classes, and some are weaker to them. The one consistent feature to duelists, is they generally counter each other. The best are generally the ones that are most difficult to play because they offer the most outplay potential. With that in mind, here are the best duelists:

Riven

Riven is an incredible duelist because of her low cooldowns, high damage and sustain, and lack of ability costs. Not to mention, Riven has an incredibly high skill requirement ability-set and mobility that can keep her on top of the enemy. The caveat to Riven's prowess in the 1v1 is exactly as just mentioned, her high skill cap. Riven is very difficult to play properly but when done correctly, she is a force to be reckoned with.

Master Yi

Master Yi is the classic low ELO 1v1 stomper. Yes, he is quite easy to play and his high damage and speed makes him very sticky. The difference maker for Master Yi in 1v1s definitely comes down to a well-timed Alpha Strike to not only deal damage, but to dodge out on key abilities from the enemy (usually to dodge crowd control, but can be just for significant damage as well).

Fiora

Like Riven, Fiora offers the same strengths, but instead of having no mana costs, she has access to tons of true damage that can really punch through the defenses of any other champion class. Like Master Yi on the other hand, Fiora must have a well-timed Riposte to really capitalize on her strengths in a 1v1 and edge out the victory. Either way, she is definitely a good choice into the tanks of this list with her true damage and ability to cancel crowd-controlling enemy abilities.

Tyrndamere

Tryndamere's abilities also cost no mana and has plenty of mobility with his critical strikes lowering its cooldown. Not to mention his ultimate basically gives him free time to hit the enemy without worry and kill (hopefully) the enemy before his ultimate is done.

Jax

As you may be able to tell, duelists all have access to some ability to deny the strengths of their enemies, either in their crowd-controlling abilities or high-damage abilities. For Jax, that is his Counter Strike. His E ability allows him dodge out on auto-attacks for the duration of the ability, and then at the end of the ability, stun enemies in his vicinity. With that combination, Jax can last the initial duration of his ability, plus the time of the stun without receiving damage from auto-attacks for the entire time.

Conclusion

When all is said and done, it's not always enough to just be in a side lane as one of these champions against a champion not included to expect to win the 1v1. It's always going to be significantly impacted by the itemizations of both champions and who can use their game knowledge to create the optimal situation to win out in a 1v1. With that in mind, if you're looking to play out the mid-to-late game in the side lanes, these champions are great options that can easily win 1v1s and style on their opponents.

Do your best and keep asking questions.

Good luck, Summoners!