Atsushi and Akutagawa have, absolutely hands down, the best relationship dynamic and development of any characters.
They started out so hateful and full of resent and anger. They found any opportunity to be at each other's throats and had to be forced by hand to work together.
They are two people who did not understand anything about the other. Akutagawa loathed Atsushi for the way he was so easily approved by the one person whose approval he needs to live.
And Atsushi hated Akutagawa for the type of person he was. All they did was fight, and there was not a single thought given about the other.
The only reason Akutagawa interacted with him in the first place was as a part of a mission where the mafia was going to sell Atsushi to another organisation.
Their relationship progressed little by little into a point where they held concern for each other even if that concern at some moments were "I am the only person allowed to kill you' it is progress nonetheless.
They actually talked with one another, even if it was yelling. They learned more about each other and their situations and created a bond.
The biggest thing about their relationship is how they literally fixed each other. Atsushi gave Akutagawa a different reason to live than just Dazais approval and Aku obviously changed as a person by being with Atsushi.
Atsushi became a person whose opinion he valued do much that he promised to stop doing his literal job and not kill anyone.
Atsushi made him a more compassionate person. He made Aku into the mafioso who doesn't kill (Odasaku parallels anyone!)
Atsushi also grew as a person. He had a lot of emotional traumas and we see those flashbacks where he panics. Eventually he becomes calmer and Dazai is a person who appears to comfort him when he panics but most recently Akutagawa was the one who appeared to help and calm him when he was losing his mind.
Atsushi thinks a lot about what would Dazai do but when he thinks of Akutagawa it's not what he would do, just thinking of him being there for him gives him strength and his panic dissipates.
Atsushi learns that Aku is someone he can rely on and trust to a point where all his worries disappear when he thinks about Aku.
Their original anger and hatred for each other are now a feeling of safety and trust, any jabs or seemingly hateful actions or words are now on the same level as Dazai and Chuuya messing with each other.
They even got to a point where they didn't need to communicate their attack plan and put their full trust in each other that they were on the same page. They put each other's lives in their hands and they succeeded (at the time, the time swords fucked that up but that's not their fault. They did great)
They truly are the only ones deserving of the title Shin Soukoku.