And here we go, into the second arc of what should be series one of this story. This arc I have decided to call: The New World According to Peter Parker
Peter is quick to become friends with everyone in Class 1-A, excelling in the quirk application test on the first day to his surprise, as he was considered a mediocre hero back in his dimension when compared to the older, more experienced pros such as the Avengers, Fantastic Four, and X-Men. On the second day, during the battle trials, Peter, thanks to his experience with defeating multiple villains before, would continue to dominate the class and come out on top of the mock battle, earning him both the praise of the rest of his class and the ire of those who would consider him their rivals, such as Todoroki and Bakugou.
However, Peter would find himself unable to relax at U.A., as he would continuously go out at night to sneak around the city in a new suit that he created known as the Stealth Suit (or Noir suit, as he called it) in order to either find the Infinity Stones or find any more of his villains. During one of these bouts, he would come across Spot and Lady Beetle looking for the Time Stone, and then defeat them and destroy their means of looking for the stones before Kurogiri rescues them. But now, with this action, Peter has placed himself in the crosshairs of All for One, and he takes up Green Goblin's suggestion to allow his men to kill him.
Meanwhile, the rest of Class 1-A votes Peter into the role of Class Representative, but upon realising that his previous (and current) profession as a vigilante might damage their public image, as well as not wanting to be in such a prominent position in the class out of a desire to keep his own public image minimal (on top of simple humbleness), Peter turns down the position and allows Yaoyorozu to take up the role of Class Representative, with Izuku becoming Vice Representative before giving up his position as well and handing it off to Iida after his handling of the break-in panic (an event that Peter would be suspicious of).
Over the next two weeks, Peter would bond with the members of Class 1-A, almost all of them eager to get to know him, especially after his performance in the battle trials where he was forced to reveal to them that he was the vigilante Spider-Man. However, this particular fact would earn him the ire of more than a few of his classmates, particularly the likes of Iida and Tsuyu due to them wanting to stick to the law, which ends up sparking many debates between Peter and the students over when a person, hero or otherwise, should take action to do what is right. Meanwhile, Peter would find himself at odds with Bakugou, who would make it a personal mission to challenge Peter whenever he got the chance. Bakugou would do this in order to gain a rival in Peter to crush. Peter wouldn't care for it.
Momo, meanwhile, would take umbrage with Peter's past as a vigilante, even if it was only the one incident that she knows about, but after seeing the work that F.E.A.S.T. has put into helping those that have been persecuted and discriminated again, as well as Kazuko's idol group endorsing it, she and Todoroki, as well as a few people from Class 1-B, would begin to discuss, with themselves and their families, setting up an organisation to help fund F.E.A.S.T..
Soon enough, Class 1-A would depart to the USJ, where the League of Villains would attack them. However, this time, instead of it being a horde of street-level villains, it is instead Shigaraki, Kurogiri, their Nomu, and Green Goblin's men.
Green Goblin would announce himself and his closest cohorts – Mysterio, Vulture, Scorpion, Rhino, and Electro – as the Sinister Six, and sent their minions, Spot, Deliah, Hydro-Man, Black Ant, Tarantula, and Lady Beetle after them.
Class 1-A and their teachers would attempt to fight back against the new League of Villains, but would be scattered by Kurogiri over the USJ, and would be hunted down by the villains. As Spider-Man is confronted and forced to take on the Sinister Six all by himself, whilst Aizawa and Thirteen are busy with Shigaraki and his Nomu, the rest of Class 1-A would be forced to content with the villains under the Sinister Six's command. They are soon forced to realise that while these villains are always being defeated by Spider-Man, they are much more dangerous than the standard street-level villain, and find themselves constantly on the backfoot. Even the Spot is able to get one up on Bakugo of all people, and he is considered the comic relief of the Sinister Six's minions. Even worse, all of these villains consider the children that they are fighting against to not be worth the effort: they're only interested in fighting Spider-Man.
This fight is meant to illustrate a point as to why Spider-Man is considered to be one of the best in the class. During his time as a vigilante and hero back in his home dimension, Peter was constantly battling against and defeating these villains, and while many of these villains are weak by Marvel standards and are always being defeated by Peter, they are still dangerous villains that ordinary civilians and police forces cannot handle.
So, against the likes of the MHA cast, especially the students, even lesser villains like Black Ant and the Spot are able to go toe-to-toe with the main characters of MHA.
TLDR; Spider-Man is one of the best of the best in U.A.'s hero course… because his villains are just as, if not even more so, dangerous as he is.
It's also my way of deconstructing the typical variant of Shounen battles, when a kid goes up against a fully grown adult. Here, what happens when a teenager with hardly any training under their belt goes up against an adult with months, perhaps even years, of experience? They get curb-stomped, hard.
During all of this, Peter finds himself to be on the backfoot against the Sinister Six, and is barely able to keep up with them as he covers Iida in making a break out of the USJ to get help, to which he then keeps his six opponents focused on him and away from the speedster. However, he is once more put on the backfoot by the Sinister Six, and is forced to retreat from them as they threaten to overwhelm him.
Meanwhile, the rest of Class 1-A are forced to rely on their numbers to try and take down the seven villains that were fighting them, but are unable to defeat the more experienced fighters and are almost beaten entirely, as is Aizawa and Thirteen against Shigaraki and his Nomu.
However, the tide of the battle soon turns against the villains when All Might and the heroes arrive. Suddenly, the six minions of the Sinister Six would be forced to content with heroes that are at their level, and the Sinister Six would be occupied by All Might, whilst Peter would soon enough go forth and use his experience with the seven villains under the Sinister Six's command to defeat them.
Soon enough. All Might goes into battle against Green Goblin, whilst Peter and his friends go up against the Nomu and defeat it. Green Goblin is unable to defeat All Might, even with the Space Stone and Reality Stones in his possession, and so he and the rest of the League of Villains retreat, meaning that the heroes have won the day. However, all the current members of the League would escape, meaning that the heroes would be taking no prisoners this day.
This would be, theoretically, where the first series of this story would end.