The successor to Nickelodeon's Avatar: the Last Airbender is The Legend of Korra, whose star (Korra) is a hotheaded Water Tribe native and a battle-hardened avatar. Unlike the monk Aang, Korra is always looking forward to a good fight, though she fights to protect the world and maintain balance. She is bold, clever, and tenacious, and can wield the four elements.
Korra can handle all the major villains in her own universe, and if she challenged characters from other animated series, she'd win against some characters and meet her match against others. Suppose Korra clashed with the characters from Fairy Tail? Let's see which of them she can defeat, and which five would triumph over the avatar.
10 Can Defeat: Bickslow
Bickslow is a member of the Thunder God Tribe, and serves as one of Laxus Dreyar's bodyguards, along with Evergreen and Fried. His magic allows him to possess other objects and control them like dolls.
These dolls can move fast, but they're nothing that Korra can't handle with her bending. She can block the dolls' ranged attacks, and most likely, she will land a serious blow on Bickslow before he even tries to use his eye magic and control Korra herself. Korra isn't one to drag out a fight, after all.
9 Can't Defeat: Acnologia
Whether in dragon form or human form, Acnologia wields titanic power, and even a large squad of Fairy Tail's best wizards is helpless before him. Acnologia lost an arm to Igneel during the Tartaros arc, but that's an exception. Most other characters can't scratch him.
Neither could Korra, though she'd give it a try. She could use airbending to elevate herself and fight Acnologia directly, but even in the avatar state, she's unlikely to deal a serious blow. In return, Acnologia could use any variety of breath attacks (or a melee attack) to take Korra out.
8 Can Defeat: Lisanna Strauss
Lisanna is the youngest of three, and like her big brother and big sister, she can use Take Over magic. In her case, she turns into a fairy typical anime cat girl, complete with ears, skimpy fur-patterned clothes, and clawed cat paws on all four limbs.
She is fairly fast and nimble like this, but Lisanna usually ends up being protected by her fellows, rather than protecting them. She wouldn't be much of a challenge for Korra at all, who could knock her away with airbending alone. Lisanna would probably concede sooner than later.
7 Can't Defeat: Mavis Vermillion
Mavis was the founder and first master of the Fairy Tail guild, and she's older than she looks. Mavis has deep knowledge of magic and the world, since she's read so many books, and used Fairy Law during combat to defeat a possessed blue dragon skeleton.
Not only that, but Mavis can also create convincing illusions, even on a large scale. In a fight, Mavis would try to scare Korra off or lure her away with illusions, and if that fails, she can wipe Korra out with Fairy Glitter or Fairy Law.
6 Can Defeat: Lucy Heartfilia
Sometimes, Lucy is unfairly teased for being "useless," though that is far from the case. Despite how often her fellows end up saving her life, she has been a hero more than once, and she turned the tide in the battle against Tartaros all by herself.
But not even the full horoscope can help Lucy against Korra, who can deal with a couple of spirits without much trouble. She could easily knock out Lucy herself, and that's going to end the battle pretty quick. Just one earthbended rock to the head should suffice.
5 Can't Defeat: Laxus Dreyar
Laxus ranks among the most powerful wizards in his guild, and he's even got loyal personal bodyguards to show what kind of respect he commands. He's an S-class wizard and the grandson of Makarov, and has proven himself against many villains, including the demon books of Zeref.
He's very tough and can deal lots of damage, and his lightning powers are sure to catch Korra unawares in a battle and stun her into submission. If he's quick, he can knock her out before the avatar state manifests itself.
4 Can Defeat: Juvia Lockser
Juvia once belonged to Phantom Lord, and joined Fairy Tail roughly around the time Gajeel did. She was one of four elemental warriors, and stood for water. Her entire body is made of it, and that makes her resistant to physical blows.
That's great, but Korra can bend water, and thus she could tear Juvia to bits just by bending her body just right. Korra's firebending (arguably her favorite element) won't do much good, but that hardly even matters; waterbending is all she needs.
3 Can't Defeat: Brandish
Brandish is one of the fearsome Spriggan 12, the minions serving their emperor Spriggan (Zeref) in the Alvarez Empire. Although Brandish is often rather lazy and goofs off, her magical power is through the roof, and even the strongest Fairy Tail members are reluctant to face her.
Her power is to reshape matter and shrink just about anything, even an entire island or just a person. With that power, she could shink down Korra to a tiny size (and shrink Korra's bending power) and crush her with ease.
2 Can Defeat: Lyon Vastia
Lyon is Ul's student alongside Gray, and since the start, he's been a proficient and elegant caster of Ice Make magic. He can create many different animated ice animals or other creations with ease, and swarm the battlefield with them.
Fighting this power won't be easy, but Korra can do it. Her own waterbending can melt the Ice Make animals, and if she goes into the avatar state, Lyon simply doesn't have the strength to survive for long. Lyon is a credit to Lamia Scale, but he's never faced the avatar.
1 Can't Defeat: Kyoka
Kyoka is a demon of the dreaded Tartaros guild, and she is not actually a wizard at all. She and the other Nine Demon Gates are Zeref's personal creations, and they wield curses rather than magic.
Curses are extraordinarily powerful, and Kyoka can modify any target's bodily attributes, such as giving herself immense strength or vastly increasing the subject's sensitivity to pain. She did all this to Erza during their fight during the Tartaros arc, for example. Avatar Korra can fight hand to hand, but if she's so vulnerable to pain, she can't fight effectively, and Kyoka could take her out.