This achievement/trophy unlocks naturally just playing through the main story campaign after the 13th mission and should be unmissable. In case you are having trouble completing the mission the following guide may help.
Grab a car and make your way to Vlad's Comrades bar. Equip a shotgun if you have one. Once you get there, Niko will confront Vlad and Vlad calls on his guys to get rid of you.
Once the cutscene has finished, kill both of Vlad's body guards with the shotgun. As soon as they're dead you'll need to sprint after Vlad who is already attempting to escape.
Chase him out of the car park on foot quickly, then get into a car as soon as you can preferably the one you parked outside, and chase him all the way to the docks, try to avoid the huge trucks that will pull out in front of you.
Eventually Vlad will crash his car and attempt to escape on foot. Get out of your car and watch the cutscene.
After the cutscene, you'll learn about executing people. Equip a pistol and lock onto Vlad. Shoot to murder him and watch the great, bloody cutscene. Right after the cutscene ends and Vlad is dead the achievement/trophy should pop.