Vendetta missions will start to appear after you complete the first Ratbag mission, around five story missions in.
In a Vendetta mission, you are tasked with hunting down an Orc who killed another player. You'll search an area to find them in Wraith mode (press [cn_LB]). Locating them will immediately reveal their weaknesses. Use the weaknesses and the terrain to plan an assault on the target.
Kill them to unlock the achievement. If you die, you will have to wait for another Vendetta mission to appear.