Adachi is a RushdownStyle of play where you constantly attack the opponent in close range fighting, never giving them an opportunity to retaliate. and pseudo-grappler character, that by nature makes himself a threat at all times with his excellent Persona usage and being able to snowball from many of his openings. He typically plays neutral out with his great Persona normals and various other moves that cover a lot of possible bases. Once he gets in, he can play a pseudo-grappling game at any time with one of his command grabs for handsome reward out of strike/throw pressure. This is on top of using his many unique special cancels to both keep an opponent locked down with unpredictable frame-traps, and open them up eventually if they attempt to escape incorrectly.
In the story, Adachi is a seemingly bumbling detective who was transferred to Inaba due to an unknown incident, and now acts as one of the main authorities on the murder cases in Inaba. He has a habit of divulging critical information to the Investigation Team, specifically to the protagonist, Yu Narukami, making him a seemingly useful ally. In BlazBlue Cross Tag Battle, he is one of the many characters summoned to the Phantom Field to take part of the Cross Tag Battle tournament.
In reality, Adachi's bumbling tendencies are not only revealed to be just an act, but he's actually the one behind the murders. Using his Persona, Magatsu Izanagi, he attempts to drag the town of Inaba into the Fog during the climax of Persona 4, but is stopped by the Investigation Team, and is arrested. In Persona 4 Arena Ultimax, he's seemingly out of jail, and reluctantly works alongside SHO Minazuki.