The first real fight, the one between Stiyl and Touma, is pretty cool in the anime and manga. But in the light novels it's narrated from Stiyl's point of view, and we see how a magician views Touma and why he becomes The Dreaded. At one point, Stiyl seriously thinks he might be fighting God.
The ending of the fight where Touma destroys Innocentius with an Offhand Backhand before running up and punching Stiyl out.
When Touma and Stiyl face off against Aureolus Izzard, a Reality Warper. After immobilizing and toying with them, he instantly completely removes all of Stiyl's skin and severs Touma's right arm, the source of his power. Touma cuts off Aureolus's subsequent Evil Laughwith an Evil Laugh of his own, walking steadily towards him—blood squirting out of his stump—with an insane smirk on his face and mocking Aureolus's frantic attacks as they pass right through him or are otherwise negated. Turns out that Aureolus's power was controlled by his thoughts, and Touma's insane behavior so terrified Aureolus that he started believing that his incredible powers had been rendered completely ineffective. By the time Touma reaches him, his imagination has granted Touma a huge dragon head in the place of his missing limb. Even after seeing his companion's skin ripped off and getting his special arm chopped off, Touma was still able to bluff his way to victory with a Slasher Smile on his face.
Before that, the 13 Knights of the Roman Catholic Church blow up Misawa Cram School... only for Aureolus to literally reverse the damage and annihilate the Knights.
The reality warping technique, Ars Magna, was thought to be impossible because one needs to chant for 100-200 years to get it. Aureolus cut that time drastically by brainwashing everybody in Misawa Cram School to chant for him.
Misaka Imouto using her powers to make ozone in an attempt to suffocate Accelerator. He saw through the tactic and attacked her, but he complimented her on finally figuring out a way to hurt him.
During Touma's fight with Accelerator when he starts making plasma, the Sisters make good use of their powers by activating wind turbines, dissolving Accelerator's plasma in the process. Complete with Theme Music Power-Up!
Touma's fight with the Unabara impostor in the construction site.
Despite having just been shot in the head, Accelerator deflects a bullet meant for Last Order—and even unconscious, he controls Yoshikawa's blood flow to keep her from dying of a destroyed coronary artery.
Touma blocking the giant stone golem Ellis' punch with one hand.
Index herself gets one when, after discovering her Sherry Cromwell decides to use her golem to attack Index and get the 103,000 grimoires that she has memorized Index then shows even without going into her emergency survival mode she has complete control over those grimores and uses them to show that the giant golem she is fighting and that Sherry's abilities aren't even on her level as she proceeds to methodically destroy the golem all while the song Jellyfish plays in the background.
Touma's Big Damn Heroes moment in episode 24 of Index, when he comes out of no where and defeats the enemy with a single punch, all while reassuring a friend. Nice.
What about Hyouka who pulls of her own Big Damn Heroes. As Index is about to get squashed by the golem she jumps at it and not only topples it but even caves in its chest. And then proceeds to stop it's fist and even pushes it back.
Touma saving Kuroko by leaping up using furniture thrown up by Mikoto was epic. Finishing it by punching a partially teleported object backwards through dimensions. There are no words.
Kuroko gets one for the fight prior to that happening. She was severely outclassed by another teleporter in all categories (including being able to teleport objects without touching them) except for speed. Had she not been wounded by her opponent's surprise attack the fight before, it's entirely possible she could have won. Even when she's pinned down she delivers a "The Reason You Suck" Speech, causing her foe to drop over 4000kg of weight on Kuroko in rage.
Immediately after above scene, Awaki was seen escaping Cue Accelerator, of all people, showing up to wreck Awaki in the face. The fight itself only lasts a minute, perhaps even less, it was that big of a Curb-Stomp Battle.
Bonus points for the conversation before the fight, when Awaki assumes she has the upper hand because Accelerator lost his powers. He correct her, saying he may have gotten weaker, but that doesn't mean she has gotten stronger... while his voice goes from calm to unhinged and he stomps the ground to create a massive shockwave that shatters all the windows in the nearby buildings.Insanity can be so awesome when it's used to Kick the Son of a Bitch...
Touma: What should I do? WHAT NONSENSE, OF COURSE I SHOULD SAVE HER!
Touma knocking Biagio Busoni's giant cross away with his left hand.
Accelerator, pissed off after a call from Kihara Amata who tells him that he holds Last Order captive and threatens to kill her, activates his remaining esper power, shoves his arm in the wall of the building besides him and THEN PROCEEDS TO THROW THE WHOLE BUILDING AGAINST ALEISTER'S FORTRESS. Just wow...
Aleister: Seems like there's some commotion outside...
In the novels, although he doesn't throw a building, he borrows a huge amount of energy from the planet's rotational vectors to fuel his attack - enough to slow it down by 5 minutes.
And as a testament to how invulnerable Aleister's fortress is, the building remains unharmed. To hammer in the point, Accelerator's attack used enough energy to slow down the Earth's rotation for five minutes! (For reference, that amount of kinetic energy would be more than enough to shatter planet Earth several times over.)
The Academy City Invasion arc as a whole can be considered a single Crowning Moment of Awesome for anyone involved. Especially for Accelerator.
Accelerator outwitting the leader of Skill-Out and defeating him. Touma vs Hamazura, a few minutes after Touma had been shot in the side.
Mr. Misaka's phone call in the end of SS2, asking someone at Academy City why girls who look exactly like his daughter have been attacking military and research targets (in an attempt to rescue the gemstones). He makes remarks about what he'd do to anyone hurting his daughter, and then the truly awesome part hits: He's talking directly to Aleister. Yes, that's right. A wandering consultant is threatening possibly the most powerful man on the planet.
During the Gemstone incident, Academy City cannot deploy fast enough to rescue them from the CIA or rely on their cooperative institutions, leaving them out of options. Well, mostly out of options.
Kumokawa Seria:I don’t like owing people favors, but we should just bow down and ask that frog to help us.
“Galashiels, UK, Higher Contact Society. Misaka has suppressed the fourth, eighth, and thirteenth domes,' reports Misaka #17000.” “Lausanne, Switzerland, World Intellectual Club. Misaka has taken out an armed guard,' says Misaka #18022 as she provides her confirmation.” “Guadalajara, Mexico, Sixth Sense Headquarters. Misaka has blown up the main entrance to the research building,' says Misaka #14333 as she heads further in.” “Deseado, Argentina, Human Sports Analysis Center. Misaka has finished taking control of the secure electronic lock,' says Misaka #15110 as she opens the route to the secret area.” “Davao, Philippines, Humanity’s Wisdom Headquarters. Misaka discovered an escape boat and is going to take care of it beforehand,' says Misaka #10090 as she begins her attack.”
Give one to Uiharu for managing not to break under Kakine's torture just before the above event, including putting her life on the line for Last Order.
Volume 16: Touma showing up to saveKanzaki and the rest of the Amakusa Catholics from Acqua of the Back when he is already heavily injured from a fight with the same person. Not only that but this gave the Amakusa Church a chance to take down Acqua with a Heroic R.R.O.D.-inducing spell.
Touma proves in Volume 17 that despite his label as one of the idiot trio, he's much smarter than he lets on. He pulls one over a terrorist by pouring boiling tea into a narrow air vent and causing it to expand, making the terrorist on the other side think that there's someone inside the air vents. The terrorist decides to check the air vent... and gets boiling hot tea poured on his face. This, by the way, was meant to distract the terrorist so Touma could enter the cargo hold through the door safely. Also, he ends the fight by giving the terrorist a lesson on thermodynamics.
Touma: “Hey, terrorist. Do you know about thermal expansion?”
Volume 18: After Fiamma steals Index's remote control, Touma simply says: “Stiyl,” Kamijou called out to the red-haired magician. “I’m gonna go punch Fiamma. While I’m gone, you take care of Index.” BADASS!
Volume 21: The combined efforts of Accelerator, Hyouka Kazakiri, and Acqua of the Back weaken and drive off Archangel Gabriel.
Volume 22: Touma drops the "Star of Bethlehem" on an Archangel. And because this was not enough, he runs through the entire thing at the same time, so HE COULD PUNCH THE ARCHANGEL PERSONALLY!
Also, when Fiamma of the Right severs Touma's right arm and absorbs it, becoming La Persona Superiore a Dio aka The Person Higher Than God. Fiamma gloats and attempts to kill Touma, but "The Invisible Thing" emerges from his stump, terrifying Fiamma. The dragon attempts to kill him, but Touma declares that he doesn't need its help and absorbs him, regenerating his arm. He proceeds to talk to Fiamma, making him doubt whether his plan was actually worth it, then charges up and punches him out.
As Fiamma is being defeated, he takes comfort in knowing he will win in the end, as a massive wave of telesma will fall on and annihilate Earth. Accelerator Awakens completely, turns into a shining angel, and reflects the wave back into space.
This might have more repercussions than you would think. By New Testament 2, Aleister is backed into a corner so deep, he took NO actions out of fear of disrupting his plans further, even when AC was about to be destroyed.
In the Short Story, Uiharu SS, Uiharu jumps atop a vehicle that's moving at 120 kph, then ties herself to it and uses a parachute to turn herself into a human brake!
In the Gemstone SS, Uiharu winds up in a hacking confrontation with Mikoto. Uiharu wins! Admittedly, by effectively destroying the data Mikoto was trying to steal, but still.
New Testament 2: Birdway got away with screwing over Aleister, and pretty much ensuring that Touma, Accelerator, and Shiage will involve themselves more in the next battle using her skills at analyzing charismatic figures. No wonder she's the author's favorite.
In New Testament 3, she's even more Badass. The other heroes are facing a magician who's basically Cinderella and curbstomping everyone, when she simply hits her with a Tanker truck and then blew it up.
Also from NT 3: Touma and Umidori defeat Saronia A. Irivika even though she paralyzed the left side of Touma's body.
And how about the president of the GODDAMN UNITED STATES OF AMERICA coming in and being a Big Damn Hero for ACCELERATOR, of all people.
"'Roberto:'" I'm the goddamn president.
New Testament 4: One-Eyed Othinus curbstomps everyone, even Touma. She severs his right arm, but when "The Invisible Thing" emerges from the stump, she curbstomps it too!!! Then, Ollerus and Fiamma of the Right arrive and manage to fight her to a draw and make her retreat.
Touma storms Baggage City and takes on Marian Slingeneyer. When Marian tries to use Dáinsleif to scare Touma to death, Touma is completely unafraid. When Marian threatens to draw Dáinsleif and trigger Ragnarok, Touma confidently points out that if she had the guts to do that, she would have done it already. She doesn't have the guts, and Touma punches her out.
New Testament 5: After being just about everyone's Unwitting Pawn since the very start of this series, Touma has finally had enough. Working with Reliable Traitor Thor to screw over all the sides this time, as well as showing off some impressive skill with The Plan such as tricking both Gremlin and Ollerus' group, specifically freakin Birdway herself, into thinking the other is setting up a trap. Looks like he's growing into quite a Magnificent Bastard isn't he?
The ending. An overzealous Anti-Skill member mistakes Touma for a bad guy and shoots him several times. He is rushed to the hospital and treated by Heaven Canceller, as usual. The doctor discusses with some people about how Touma will be handed over to Anti-Skill when he recovers. Touma, who was conscious the whole time, escapes from the hospital despite still being in serious pain.
New Testament 6: The whole novel is a huge one for Mugino, who gets past all her fears and doubts, allowing her to curbstomp a guy pulling a Shape Shifter Guilt Trip on her. She declares that she loves Shiage and that love has made her stronger than ever. Then, she teams up with Accelerator to take on Kakine. The fight ends with Beetle 05 declaring that he is Kakine, taking over all of Kakine's Dark Matter creations, and erasing the original from existence.
Touma, still weakened from having been shot several times, fights back-to-back battles against Leivinia and Thor, even breaking Thor's wrists. Then, Touma figures out how to cure Fraulein's Horror Hunger.
4. The battle between the Level 5s and the 7500 "heroes"... Or better said, the Curb-Stomp Battle. Accelerator alone defeats 1000 just with his Dynamic Entry, Gunha is more concerned about preventing the forest fire, Mugino blows up a truck and then makes small talk with ITEM, and Misaki and Mikoto are spending more time bitching to each other. Oh, and that person who everyone thinks is the #6? Actually, just some Badass Normal whose punches are described as "like machine pistons"!
5. Kakine showing his new merit as Big Damn Hero, saving the day and fighting side at side with Touma against Rensa #29.
6. Fremea finally deciding to stand up for herself instead of waiting for a hero to save her and hacking the city's AIM field despite being a mere Level 0.
New Testament 8:
Loki anticipated a spy would infiltrate GREMLIN's base, so he placed an artificial sky over it so that Ollerus would read the wrong stars and give his allies the wrong directions.
Touma and Freyja's Traintop Battle. When she sends her army of monsters at him, he negates one, crushes one underfoot, then tackles one so hard it flies into the others and knocks them all off the train. Later, when Freyja thinks she's knocked Touma off the train, he reveals he hung on, then throws his jacket over her head to blind her.
Mikoto lands gently from a plane sliced in half while catching Index, leaps from building to building too fast for an interception spell to keep up, and blasts Níðhöggr to pieces with a volley of coins. She even has the attention to spare to feel bad about upsetting Sphinx with her magnetism.
New Testament 9:
Some people set fire to the house Touma is in. Touma jumps from the second floor and lands on them, knocking them out cold.
Touma defeating a crazed Pierce Aogami after suffering a broken arm.
Though it was undone by the Will of the Misaka Network, Othinus did what no other antagonist did before. She made Touma give up hope.
Touma: "It's time to bring this to an end. It's time to fight a god."
Touma, after purposefully dying in battle against Othinus thousands of times, uses his experience from that to dodge all of Othinus's attacks and then punch out Gungnir while only breaking two of his fingers.
Othinus unleashes a crossbow bigger than the planet and fires ten arrows at Touma. The first one comes straight down, the second comes from behind him, the third and fourth come out of the ground, the fifth comes from in front of him, the sixth and seventh use Robo Teching, the eight teleports, and the ninth turns into a Rain of Arrows. Touma dodges or deflects them all, only for her to fire the tenth one through her own body to finally hit him.
In the end, Touma was simply unable to defeat Othinus in a fight, but he still wins by convincing her to pull a Heel–Face Turn.
Now back in their original world, Othinus is the enemy of the world that EVERYONE is gunning for. Be that as it may, Touma doesn't hesitate in placing himself in front of her and taking up the enmity of the world.
Accelerator No Sells a punch from Touma for the first time.
Touma knocks Accelerator out by smashing a rock into his own hand give it enough velocity to pierce his defenses. He does this as a counter to a 5000 meter instant dive bomb attack!
Touma defeats various apocalyptic beings like Surtr that Marian summons.
Touma beats the President of the United States in a debate, while having a gun to his head.
The FIVE_OVER program was created to make weapons more powerful than the Level Five Espers, and 150 of the Railgun models are sent after Touma. Mikoto hijacks all of them.
Touma tricks Thor into stepping in front of a train.
For the first time since the beginning of New Testament, Touma says his classic, "Then I'll destroy that illusion!!!!"
The True GREMLIN group suddenly make an appearance, rescued Othinus from her own suicide while calling her (i.e. a nigh-omnipotent goddess at this point) a failed experiment. They proceed to say that she didn't even know the true purpose of GREMLIN which is actually comprised of the Magic Gods from every religion of the world (!!!), and it's revealed that they are manipulating the growth of Touma as a main part of their plans. Chessmastery at its best.
Right after the above, when the Gods finish talking to each other and are about to leave, Aleister suddenly destroys the barrier between dimensions to access their Phase. He says that he used their own rescue of Othinus to figure out their untraceable location and that his plan is apparently back on track. The apparent leader of the Magic Gods then responds and confronts Aleister about his actions and goals. This Magic God proceeds to mock Aleister, implying that his current goals have to do with "the single remaining tearstain" in his journal. Aleister, who never seems to show any emotion at all, seems stunned for a few moments... and then he takes his Blasting Rod (you know, the object he used to one-shot the One Above God), says his magic name (Beast 666) and prepares to attack them...When he does this, instead of running away, the Magic Gods make fun of his emotional response and his "humanity" and then proceed to reveal that they know about Aiwass (the super secret cornerstone of his plan, up until now is the most powerful entity in the series) and say "It’s a complete failure, young one. You’re going to be at your wits’ end before long." This drives Aleister to attack them, but the results are not seen until the next two volumes. Crowning Moment of Awesome for them.
New Testament 11:
An esper-hating gang called Deadlock targeted Misaki for termination. They ride around on rocket-powered roller skates, moving too fast for her to target with her mental powers. Touma nonchalantly chucks a remote control at one member's head and makes him crash. He then kicked all their asses, even though they were all armed with hand-held pile bunkers.
Some mooks pretending to be paramedics tell Misaki to come with them, but she sees through their ruse. They then attack her, but she uses her powers to make them see each other as her, so they knock each other out until there is one left. She then makes him think she is his boss.
Aleister actually surviving the battle against the Magic Gods, although he was badly burnt, he was still fighting against bona-fidegods, and survives.
New Testament 12:
Touma vs Shiage fight each other over how to deal with St. Germain, a self-proclaimed Magic God. Despite Shiage using a Power Lifter Touma stills manages to force him out of it and turn it into a normal brawl. Shiage manages to win by using one of the Power Lifter parts.
In the climax fight against St. Germain, Touma completely breaks his composure by revealing his true nature as a con artist and exposing all his lies.
Three Magic Gods from True GREMLIN have arrived to AC and are about to start their plans in the real world. Crowley speaks with them through a speaker, and they taunt him, reminding him of his defeat in their previous fight. They even tell him that now would be the perfect time to defeat him because they were forced to weaken themselves with a spell in order to be able to act in the wold without destroying it, all while completely confident in their superiority over a 'simple human' like Crowley. Crowly calmly informs them that he already knew they were coming and uses their own spell to overwrite their structures and change their parameters. When the High Priest questions where he got their data for the spell Aleister reveals that the fight against them in their Phase and him getting angry at the mention of his journal were all just an act. High Priest points out that even then he would still have to have beaten the Magic God who cast the spell in order to change it. Said Magic God promptly falls from the sky in front of them nailed to a rosy cross. Crowley tells them that he no longer views them as a threat and and that they need to remember what death feels like.
Aleister: I would prefer not to use such inelegant language, but by any chance, were you taking me for a fool?
New Testament Volume 13
Touma and Mikoto defeating the High Priest, a Magic God, using Science of all things, by essentially blasting him into space with the biggest Railgun ever.
Kihara Noukan using a giant drill to finally kill the High Priest when it tries to return to Earth in a comet.
After the death of the High Priest, Niang-Niang prepares to destroy Academy City out of a desire for revenge. Just before she does it she's interrupted by Kamisato Kakeru, another boy with a special right hand. Kakeru proceeds to use his right hand, World Rejecter, to casually defeat both Niang-Niang and Nephthys by sending them to a "new world", while revealing he had already hunted all the other Magic Gods from Gremlin. Nephthys can barely ask what he is before he almost finishes her, only avoiding the same fate as Niang-Niang thanks to her organs being separated from her body.