To unlock the Disorganised Crime trophy in Spider-Man The City That Never Sleeps: The Heist, you just need to complete at least five Maggia crimes in a district in the DLC. Note that the DLC doesn't trigger any new crimes in the Harlem district or along the southern edge of the island -- everything takes place in the centre.
Maggia crimes are pretty much like Fisk, Demon or Prisoner crimes in the main game; there are car chases or groups of enemies assaulting an intersection, roof or store. There are two slight variations; Spider-Bot missions in which you must defuse a series of car bombs with Spider-Bot (these are incredibly easy, don't worry at all about the timer), and Kidnap Victim missions in which, instead of finding the kidnap victim and then defeating the enemies (as in the main game) you will defeat the enemies and then chase down the car with the victim.
Otherwise, this is very simple and familiar. As soon as you complete five Crimes in one District the trophy will unlock. Note that you need to complete all Crimes in all districts that require it in order to unlock this trophy: