Unlike the main story campaign, you will have to defeat all 5 of the DLC warchiefs in a specific order. Each story mission starts out with a tutorial on a new way to control the beats in the world which include mounting wretched graugs and branding Ghuls. You then have to use what you have learned to draw out the next warchief. You are free to kill said warchief in any way that you see fit however. The 5 main missions are as follows...
Call of the Caragath - get 5 stealth kills mounted on a caragath without setting off an alarm to draw out the warchief and then kill him. (you CAN be spotted, just kill any enemies before they set off the alarm)
No Rest For the Wretched - projectile vomit 20 archers with a wretched graug to draw out the warchief. (be sure to eat enemies on the ground to replenish your health as projectile vomiting drains your health bar)
Blasted Uruks! – chase and kill 10 enemies transporting explosives while mounted on a caragoth to draw the warchief out. (run fast and don't waste your arrows as they are the easiest way to dispatch enemies at high speed while mounted)
Stronghold Uprising – bait 3 mounds of ghuls inside the warchiefs stronghold to draw him out.
Homewrecker – lead an army of branded ghuls into the warchiefs cave to fish him out. After you have taken about half his health down he escapes outside and you battle him again. The final warchief is actually quite easy if you concentrate on only branding the surrounding monsters and letting THEM do the dirty work for you. The battle starts out with an endless spawn of ghulls swarming the area. After a bit of damage has been done, Caragaths start to show up and then a wretched graug. Keep branding these monsters and they will take out the warchief (and net you the achievement) in no time.