Psychopaths are human bosses you can find and beat in to progress cases and get powerful new gear. These opponents are people who've gone insane from the stress of the zombie outbreak, attacking you and sometimes keeping other survivors hostage.
You need to take down some Psychopaths to move the story forward, but some can only be encountered at specific times. Some of the Endings in are tied to solving every Scoop case in the game.
The can only be reached in Overtime mode, a continuation of the 72-hour mode story you can only achieve by completing all cases.
To do this, you need to know how to find certain Psychopaths fast, and how to take them down quickly before moving on to another one.
Around 15 Psychopaths total are in the game, with many being familiar to those who played the original. These bosses are found in specific locations around the Mall, but can only be encountered at specific times.