Akira is pickpocketed by the girl, Argo, and is stopped by Katsuya and gang. Katsuya steps in to protect her and Akira is forced back due to the difference in numbers. He is extremely frustrated with himself, because getting pickpocketed by some nobody from the slums is the very representation of what he's been trying to avoid by training like madman: the weakness of his past self. Not only that, he just came back from a successful job, rewarded by the city, thinking that he's getting stronger and moving on from his weak self of the past, and then the pickpocketing happens and he absolutely flips out. Alpha talks to him about it, then Akira realizes his reaction was a little overboard. So he compromises by promising Alpha that he won't actively search for Argo. Instead, he informs Sheryl's gang and lets them find Argo for him. If they do find her, he will off her then. If not, he won't do anything.
Scene cut to when Argo is trying to join the gang. Her friend in the gang, the one Argo was giving the 100k aurums to in the manga, gets word of Akira looking for a pickpocket that stole his money. She quickly realizes that Akira is looking for Argo and tells her to leave quickly after admonishing her for doing something so reckless. Argo escapes and runs to Katsuya for protection, who attempts to have her inducted into Drankam. They refuse because they think it's a terrible investment, and Argo ends up living in some building outside of the Drankam complex. As stated above, after Akira is pickpocketed, rumors of an easy hunter mark spreads in the slums and Akira is constantly plagued by pickpockets, and he incapacitates all of them easily. But these events only make him much angrier and resentful, ensuring that he will never forget his promise.
Both Sheryl and Argo are eventually kidnapped by a slum gang hoping to use the both of them to threaten Katsuya and Akira. Naturally, the both of them set out to save them, and they do end up meeting each other due to the machinations of a lady who might be introduced later in the story. I say might because she was in the WN, but may have been removed from the LN. There's a heartwarming scene of them working together to fight their way through the gang compound, until Akira comes across Argo. Remembering his promise from before, he ends up killing her in front of Katsuya, forever cementing their relationship as irreconcilable enemies. Akira finally cuts off one of the links to his weak self of the past, but it's not over yet.
Scene cut to Katsuya and Akira confrontation. A bunch of irrelevant events happen, and Katsuya and Akira eventually meet each other in the field. After Akira incapacitates Katsuya's Drankam team, they end up in a sword fight in the Mist, which inhibits Akira's connection with Alpha. Lacking her support, Akira is forced to rely completely on his training and experience to duel Katsuya. He utilizes everything, even that slow-mode skill we saw a few chapters ago, and eventually bisects Katsuya from head to toe. This is important because this is the very first time he fought against an overwhelming enemy force without Alpha's help, representing his true first step towards being a strong hunter. It also represents him finally cutting the last link to his weak self, because previously he was never able to fight Katsuya due to the difference in numbers and Akira's lack of confidence. Naturally, his transition into a strong hunter who doesn't need Alpha's help all the time is marked by a train ride to a city closer to the Frontlines, his ultimate objective.