It would be rather boring if shonen characters won all their fights, but it would be equally tedious if they weren't given a single chance, either. The role of the heroes is to ultimately — and after exerting a great deal of effort — defeat and/or destroy the villains, so that's one battle that they are expected to come out of successfully.
However, there have been a few clashes in which the hero has not been readied (by their mentor, perhaps) to face their nemesis, and they are only handed victory due to unpredictable plot twists or instances of deus ex machina to rush things along. In other words, the realism of outcome in some cases does not really feel foolproof.
10 Bleach — Ichigo Vs. Aizen
Sosuke Aizen's fourth Hollow form, as granted to him by the Hougyoku, is a monstrous amalgamation of Hollow and Shinigami. A solitary cero produced by this creature is enough to evaporate a city-sized area and leave an unfathomable crater behind.
Still, Ichigo wins this one without even trying — all he needs to do is spend three months of his life performing some arcane art of zanpakuto meditation in order to obtain the one power, that the protagonist naturally possesses, of course, to defeat Aizen.
9 Hunter x Hunter — Gon Vs. Neferpitou
In all fairness, Gon himself certainly doesn't believe himself anywhere near strong enough to take on the likes of Neferpitou (a Chimera Ant that Netero is wary of).
The plot allows him to extract his future into the present, converting him into the most powerful version of himself, regardless of having his life reduced. Neferpitou is no match for the older Gon, who destroys her with as much violence as she had earlier inflicted on his beloved Kite.
8 Demon Slayer — Tanjiro Vs. Rui
Tanjiro's attempts to protect Nezuko from the Lower Moon Rui is a terribly daunting task, and the young demon slayer doesn't quite possess the confidence to do so. When his sister is ensnared and tortured, the hero is provoked into attacking his opponent out of love for her.
It must be stated that Tanjiro's flame-enhanced Water Breathing Form Ten is still incapable of killing Rui, as the demon slyly takes the right precautions. Before he and Nezuko are brutally killed, though, the villain is calmly taken out by a Giyu Tomioka.
7 My Hero Academia — Deku Vs. Muscular
Midoriya Izuku's eagerness to befriend Kota leads to the child pushing him away further, but right as they develop a slight semblance of friendship, Muscular enters the scene, pompously challenging anyone who wants to fight him.
The enemy is far too strong for the student, and he gets kicked around quite a lot, nearly dying in the process. Of course, Kota's attempt to "save" him is what energizes Deku into multiplying two of his techniques together and one-shotting Muscular, at great risk to the former's body.
6 Kill La Kill — Ryuko Vs. Harime Nui
Harime Nui, Ragyo's main minion, is composed of the same life fibers that have gone into Ryuko Matoi (except the Grand Couturier isn't human at all). In fact, the hero's mother had already brainwashed her by that point, so breaking out of it takes some help from the gang, chiefly Mako.
Once this occurs, however, Ryuko is back to her original personality, and suddenly receives an extremely large influx of power. Nui can't do much except flail around in fury when her arms get sliced off.
5 Fullmetal Alchemist: Brotherhood — Edward Vs. Father
The final battle in the series takes place technically between Father and Mustang, Hawkeye, Armstrong, Lan Fan, a couple of Chimera Warriors, Izumi Curtis, the whole Briggs Batallion, and Edward (with a crucial cameo appearance by Greed/Ling).
Everyone works together to weaken Father and deplete his Philosopher's Stone, Alphonse sacrifices his soul to restore Ed's lost limbs, and Greed converts daddy's body into graphite. Only then does Edward's punch take effect, forcing his opponent back into the formless void he had arisen from.
4 Yu Yu Hakusho — Yusuke Vs. Rando
Rando, with complete knowledge of 99 styles of martial art, is ridiculously overpowered; Yusuke's Spirit Gun has little effect, so he resorts to a physical attack. Unfortunately, this leaves him completely open, so the demon decides to use the Shrinking Curse on him.
Shockingly, it is he who starts reducing in size, and it falls to Genkai to explain that mantras need to be audible to targets for them to work. Yusuke's intelligent ploy of sealing his ears with a clump of algae saves the day, and his life.
3 Neon Genesis Evangelion — Unit-01 Vs. Sachiel
Gendo Ikari mercilessly manipulates his only son into fighting off an Angel, heedless of the fact that Shinji has had zero experience piloting an Evangelion. As expected, the boy fails miserably, but right before he is actually killed, he loses consciousness.
When he wakes up later, he is told that Unit-01 had self-activated and crushed Sachiel into nothingness, which is later revealed (sort of) to be the work of his mother, Yui Ikari's soul ensconced within the mecha.
2 My Hero Academia — Mineta Vs. Midnight
Mineta Minoru is quite the irritating character, but it can never be said that he loses his wits in a fight. When faced with Midnight, a Pro-Hero with an all-pervading power, he seemingly runs away like a coward.
The truth of the matter is that Mineta's plan of sealing his mouth with Hanta Sero's tape gives him temporary immunity to his opponent's sleep-inducing scent. He combines this tactic with a ton of Pop Off Balls that practically glues Midnight into immobility. Probably one of the biggest twists of the UA First Term Final Exam.
1 Bleach — Ichigo Vs. Yhwach
If Aizen wasn't overwhelming enough, Ichigo's final enemy turns out to be nothing less than an omnipotent God — Yhwach, whose Almighty was already untouchable before he swallows the Soul King.
Then again, the protagonist succeeds not because of his own reiatsu or talents or even genetics, but because two close friends and one mortal enemy assist him in battle. Renji distracts him, Aizen hypnotizes him, and Uryuu turns him mortal, allowing Ichigo's slash to cut Yhwach in half.