Mafia III: Definitive Edition

This achievement is story related and unlocks during the French Ward missions. After you secure the French Ward rackets--Sex and Drugs--the Kill the Judge mission becomes available. Lincoln meets with Donovan and finds out that the Judge rides in a very tough (but not completely impregnable) armored vehicle and that he varies his route.

Whereas the game suggests that Lincoln tail the judge and ambush him, it is much simpler to put a booby trap in the road before the Judge sets out. Open the weapon wheel by pressing then cycle through the explosives using until C4 is the current explosive. Lincoln only has to walk a few steps to place a C4 charge on the road near where the Judge will begin his route. Place the C4 charge by pressing followed by .

After placing the C4 charge, Lincoln gets in a red De’Leo Traviata that is conveniently parked on the corner. He starts off looking over his shoulder. As soon as the Judge's armored car gets to the explosive, Lincoln detonates the C4 charge by pressing . Note that the control for detonating the C4 while in a vehicle differs from detonating it while on foot.

If successful, a banner will appear stating, "Kill the Judge--Escape." Lincoln then has to escape the police cordon. The De’Leo can easily outrun the police cars or he can use an associate. When the cordon is cleared a banner will appear stating Kill the Judge is complete followed by another banner stating that the story mission Kill “Uncle” Lou Marcano has been unlocked. The achievement will pop after these two banners appear.

The mission can be accomplished in any number of ways. Lincoln can tail the armored vehicle and ambush it using his car, grenades, rocket launcher (if available), etc. I recommend the booby trap approach described above and demonstrated in the below video. Lincoln does not have to deal with the Judge's police protection before or during the assassination and gets a head start escaping the cordon following the kill:

Very easy mission if you've got the rocket launcher. C4 or other explosives should work as well, the rocket launcher just has the best range.

Wait for the judges car and police escort to leave the courthouse and follow them. The usual tailing rules don't seem to apply as I got quite close at times with no issue. Just make sure you don't hit them.

Eventually the police escort will peel off and the judges car will go into an alley and meet with a drug dealer. While they're stopped, hit the car with the rocket launcher. Escape the area - no police should chase you - to earn another achievement.