Bartender is a subversion. The main character has already travelled the world and been apprenticed to the most famous and skilled masters of his craft in the world by the time the manga begins. When it begins, he has come to the conclusion that he has learned everything he can, and is ready to set out on his own.
In this case, the "long running" and "unobtainable" parts are implicitly justified. Not only does Akio not intend anyone but himself to obtain the power, but his methods are horribly flawed (horrible and flawed separately) and he just keeps going at it every time the previous iteration of the duels fail.
A Tournament Arc was introduced in Love Witch which would award any wish to the winner, even if it contradicted regular witch rules. Ai is all over this, and the story looks like it's heading in the direction of To Be a Master... but then the manga got canceled before she could even enter.
In Attack No. 1, an early volleyball anime, the goal is naturally to win, but every girl on the team covets the No. 1 jersey, which is basically the title of MVP.
Fist of the North Star is sort of an Unbuilt Trope when it comes to this, in that the ultimate goal of the main antagonist is to be the best martial artist ever, and become powerful enough to conquer even the heavens. This leads to him becoming an evil, power-hungry tyrant, on top of being a Tragic Hero.
In One Piece, this is the stated goal of Luffy, who wants to become King of the Pirates, and Zoro, who strives to become The World's Greatest Swordsman.
Hell, this could be the stated goal for almost every single Straw Hat: Nami wants to become the world's greatest cartographer by charting a map of the world, Chopper wants to be the world's greatest doctor who can cure any disease, Franky wants to become the world's greatest shipwright... Even the heroes that don't have 'the best (blank)' as their goal still have the ideal in mind by getting whatever it is they're trying to find.
The Hokage ("Fire Shadow", in other words, the head ninja of the main character's village) in Naruto. The title character originally had this goal because he wanted respect and thought it would easily solve all his problems. Since the Invasion of Pain, Naruto has gained a slightly more realistic idea of the position and becoming Hokage has instead become simply one (probable) step towards his new goal: world peace.
The King of Shamans in Shaman King. Yoh wants to become Shaman King so that he can lead a life of luxury and relaxation. His arranged fiance also wants the same things. Oddly enough, they work HARD (Though Anna frequently has to bully Yoh to do so) for the ability to lie around all day.
The King of Games or Duel Champion in Yu-Gi-Oh!. Note that in the original series and in Yu-Gi-Oh! 5Ds, it wasn't the protagonist who sought the title of the best player as his primary goal (though they got it anyway, and pretty early on). Yu-Gi-Oh! GX and Yu-Gi-Oh! ZEXAL, however, follow the more traditional format with a hero whose explicit goal is to become the next King of Games/Duel Champion.
The title of "Pokemon Master" in Pokémon. In practice, Ash's usual goal throughout the anime is to be the champion of the current region's Pokemon League. Succeeding in this might cause Ash to consider himself a Master, but who knows?
Especially considering that Scott offers him Frontier Brain status when he beats the seventh (and last) Frontier Brain of the Kanto Battle Frontier, making him a de facto Pokemon Master, but Ash turns it down to continue his journey in Sinnoh instead.
He actually does have a lot more to learn, and will continue to do so for as long as they make the anime. He hasn't won a single league aside from the Orange Island filler season, hasn't caught anywhere near the amount of Pokemon that are in each region, not to mention the ones that get Put on a Bus. He could be considered something to the effect of one of the game's Ace Trainers, but he still loses plenty of battles. He can't even beat any of his rivals until the Leagues, as he was only able to definitely beat Gary in the Johto League. Even though he's been able to beat Paul twice, those were both flukes that were the products of a Deus ex Machina and even in a six-on-six battle still lost horribly. Ash finally beats Paul in the Sinnoh League.
Actually, Ash Ketchum could be considered a very powerful trainer, even quite near that of a master. In the Original Series he proved to be inexperienced and overconfident, but as time went on, he has improved dramatically. True, in recent days he has not shown much interest in catching all of the pokemon in the world, but he has defeated a large sum of enemies previously thought to be unbeatable, and his CV includes having saved the world over seventeen times, defeating four different legendary pokemon, shutting down multiple international crime syndicates, and having defeated all of the Frontier Brains (as mentioned above), which Elite Four member Agatha claims are as powerful as the Elite Four themselves. On top of all of this, Ash's loss in the Sinnoh League (the most recent of his attempts at a victory) can be labeled as a Diabolus ex Machina at best. A character was written in out of nowhere with two legendary pokemon just so he could defeat Ash. Most of Ash's losses these days are due to the writers, not his abilities. A good example of this would be how Ash's Pikachu seems to magically get weaker each time he travels to a different region.
In Pokémon Special, this is the goal of at least one protagonist per generation, in some way or another. Those that specifically want to be Pokemon Masters are Red and Green. Others that do the gym challenges and/or the battle frontiers are Sapphire, Emerald and Platinum. The ultimate Pokemon catcher would be Crystal, completing all the Pokedexes she is given minus the legendaries. The one who wants to be the best Coordinator is Ruby, who competes with Sapphire to see who can be a master first. Lastly, the concept is parodied with Diamond and Pearl, whose goal is To Be a Master of the Boke and Tsukkomi Routine.
Black wants to be a Pokemon master as well. In fact, this is all he ever thinks about. His mind is so one-track on his goal that he needs his Munna to eat away at his dreams when there's a more immediate problem.
Pretty much every sports series out there will have victory in one or more Tournament Arcs as the goal:
Subverted as of Chapter 63 when Soul Eater finally eats a witch's soul and becomes a death scythe.
And then has several characters point out that attaining the rank actually leads to more responsibility and more challenges, rather leaving the impression that in the wider scheme of things not much has changed. A curious take on something that was presented as the series' goal, to see Soul appear to be one of many in the same position (there are, after all, Weapon students around the world).
Spoofed in Rune Soldier: Louie is a magic-user who trains to be a consummate master...of hand-to-hand combat.
G Gundam, everyone's fighting to put their colony in control of the Earth by Gundam gladiatoral conflict.
Oban Star Racers: The winner of the titular races gets to be the Avatar. The thing is, everyone in the races believes that the prize is the granting of whatever they wish.
The Bees in Letter Bee, are trying to become Head Bee, the most skilled of the Bees who often works in the capital(living in the capital in and of itself is a great privilege). Gauche Suede in particular wants to become Head Bee in order to get money to heal his youngersister Sylvette's legs. However, this is a subversion, as it ends up not being the main point of the story.
Hikaru no Go actually averts this; Hikaru gets into the game of Go just for the fun of it, and just happens to be in the running for the best player of his generation (the fact that he wants to be a worthy opponent for the prodigy Akira also helps). Hikaru himself acknowledges that he is part of the eternal search for "Kami no Itte" (literally, "Hand of God", but often translated as "Divine Move"; both refer to playing a perfect game) but this goal is more spiritual than something that can actually be achieved.
In a very twisted way, Death Note is exactly this: a young, idealistic protagonist wants to be God. In terms of being a 'Master', you don't get much higher than that.
Angelic Layer, even if it starts the main character out with unexpectedly showing off her talent at the game.
Hajime No Ippo (Fighting Spirit in the West) features Ippo, a young man who desires to be first Japanese Featherweight Champion, and then World Featherweight Champion. He's been trying since the early 1990s.
Subverted in Kenichi: The Mightiest Disciple. Kenichi is training to be a master of.. well ALL the martial arts, but instead of training for the purpose of becoming a master, he trains in order to prevent people picking on him and to be able to protect his loved ones.
Harry James-Potter-Evans-Verres of Harry Potter and the Methods of Rationality wants to become the most powerful wizard in existence and rewrite reality according to his will. And with both of the current contenders for the title being his mentors, he just might pull it off.
Star Wars: Much of Luke Skywalker's character arc in the films can be summed up as "Luke trains to become a Jedi Knight like his father." Much of the rest of his character arc centers around learning about his father. While he starts training early in A New Hope, he doesn't officially become a Jedi Knight until the end of Return of the Jedi, just before confronting the Big Bad.
This character arc is mirrored somewhat by Anakin Skywalker's arc in the prequel trilogy. He leaves his homeworld to train to be a Jedi in the first film, and by the end of the third film, he has become a Dark Lord of the Sith.
The aesop of the song "Hall of Fame" by The Script is to live your life as if this trope is in full effect, for whatever path you choose to follow.
The underlying goal of almost every wrestler ever. As Triple H once put it, "If you're not here to be champion, you're in the wrong place." That said, there are more than a few wrestlers who don't seem to be in the right place, by Trips' standards.
This is the goal of countless Real Life athletes who dream of winning the gold medal, the Vince Lombardi Trophy, the green jacket, the Stanley Cup, or whichever other award is given for their sport. You don't have to be a pro to do this either, since many high schools and colleges will pursue their own championships just as rabidly as any big league athlete, if not more so.
Basically the whole motivation behind professional fighting sports. To be a champion is the ultimate sign of ability. With the belt comes the money and fame that gives even more incentive to be the champ.
This is subverted rather nastily as it turns out that, despite what Prier thinks, "Maiden of Light" is the Chosen One instead of a title to be earned. And the only "perk" is that you have to end up making a Heroic Sacrifice.
Probably explains her later career shift to Overlord. Quite possible as polar opposite a job as you can get without becoming the Dark Prince.
Blatantly done in the Pokemon games. Sure, you prevented the destruction of the entire world. But you haven't beaten the game until you've become the League Champion.
And won the Master Rank Super Contest in all five categories. And Caught Em All.
Even then no one recognizes your achievement,and the last champion still has to fight you. Though this is subverted slightly in Red/Blue and their remakes (FireRed and LeafGreen), where you are proven to be the Champion, but you still fight your rival.
The Championship uses a nonlethal form of Klingon Promotion. You become Champion by defeating the incumbent champion (your rival in Red/Blue and its remakes (and Green and Yellow), Lance in Gold/Silver and its remakes, Steven in Ruby/Sapphire, Wallace in Emerald, Cynthia in Diamond/Pearl and Platinum, and Alder in Black/White). The Elite Four just test if you're qualified to fight the Champion at all (or in pure gameplay terms they serve to sap your Pokemon's strength and make the final battle harder). Even after the Elite Four you're still a challenger until you knock off the current Champion. And even after you beat the Champion, most people act like you didn't.
Pokemon Black And White double subverts the champion part. Instead of having you fight the champion for the main story, the leader of the villain team actually beats the previous Champ, raises a giant castle near the Elite Four area, and thus proceeds to a Boss Rush for the main ending, with you first fighting the version legendary that you can catch, then fighting N, who uses a team of the other version legend and 5 other set Pokemon, and finally fighting Ghetsis, who turns out to be the real villain. Still, the post story also lets you rematch the Elite Four, who then have you fight the actual Champion (this is the double subversion part), along with (outside of the Unova Pokemon league overall) Cynthia and Shigeki Morimoto.
Deconstructed by your rival Cheren from the same games. Over the course of the game he slowly learns that being the best for purely the sake of it is completely pointless. Later Reconstructed when he seeks out a reason to be the best and, two years later, becomes a gym leader.
In Growlanser 2, Wein's goal is to become an Imperial Knight. Whether he accomplishes this depends on what branches of the story you take. And even if he gets the title, the plot has long since moved on to more important matters, like the fate of the world.
Homeworld 2 has an ancient prophecy about the three Great Hyperspace Cores awakening Sajuuk, the god of destiny and creation (actually, a big-ass ancient starship hidden in a black hole cluster). Supposedly, the one who unites the Three will get to be the Sajuuk-khar, Manipulator of the Great Maker. When Karan Sjet first hears about it while running from the Vaygr, she deduces that Makaan must also know about it and seek to aquire both the Bentusi and the Hiigaran core. Naturally, the world is doomed if he succeeds so she decides to beat him to it. The thing is, by doing that she accidentally fulfilled the prophecy herself and became the Sajuuk-khar - which proved really useful when Hiigara was attacked by Planet Killers whose armor was impeneterable to every weapon except Sajuuk's Wave Motion Gun. With the ship also activating an ancient hypergate network spanning the galaxy and having the most powerful weapons & hyperdrives of the known universe, she was practically worshipped as a living goddess (her people never became atheists during their troubled history).
Choro Q HG 4, you and your rival work the ways to become the best racers.
The unstated goal of Elite is to achieve the eponymous "Elite" rating. As the game is one of the first ever examples of a Wide-Open Sandbox, nothing particularly compels you to spend the relevant time Level Grinding to achieve this, but legitimately doing so earns some bragging rights.
This is the basic goal of the Punch-Out!! games. The new Wii game takes it to the next level-after Little Mac wins the championships, he's then forced to defend his newly won titles against disgruntled opponents looking for a rematch.
Fossil Fighters toys with this. You are trying To Be a Master—and you become one! In fact, you become one only about halfway through the game. However, as it turns out, there is still a lot more going on despite your mastery, and you will have to actually use your master's skills.
Summon Night: Swordcraft Story - The first Swordcraft Story game's overall focus is mostly about becoming a "Craftlord", which is basically a "Master" of weapon crafting/fighting. There's still a plot and antagonist, but the game doesn't end until you become Champion. The game's two successors still retain this trope to some degree, but it's downplayed quite a bit compared to the first.
Live A Live's modern chapter. Four words: -Strongest in the World-.
Rikochet of ˇMucha Lucha!. His ambition is to become the greatest of Luchadores.