After taking over two rackets in the French Ward, this quest will become available. You have time to prepare so make sure to get your best weapons before talking to Donovan. Head to the location marked on your map to talk to Donovan to start a cutscene.
The judge will be escorted by police patrol cars. You can use the police dispatcher associate when you’re ready to strike. You can also attempt your assassination while they on the road but this can be very risky. Also, you can tail the convoy but you have to make sure not to commit any crime or hit the patrol cars.
The patrol car escorts will drop off one by one until the judge makes his first stop inside a compound with enemies. This is actually the best time to kill him. Follow them inside then ready your weapon. Lob a grenade or two at the car then shower it with bullets until you kill the judge and everyone inside. Once done, leave the area quickly until you get out of the range of the circle in your minimap.