1 Kill the guarding captains first
The first thing you need to keep in mind is that every war chief would have two captains who guard them. So, you need to identify them, and before you start, the captain first kills them to be safe.
2 Don't begin the mission with the captains alive
It is always good to kill them in the beginning as it would become tough for you to kill them in the middle of the game. Also, it becomes difficult to kill all of them together.
3 Identify guarding captains against the army screen
Once you kill them after that, go to the army screen and pick the Warchief that you wish to kill. As you destroy them, there would be two lines coming out of Warchief that would lead towards the captains who safeguard them.
4 Finish the captain related missions first
For almost all captains, there is a purpose that enables you to kill the captain without any trouble in a comparatively secluded area. (See How to interrogate enemies in Shadow of Mordor?)
5 Lure the Warchief out of the stronghold
It does not imply with all Warchiefs, but you can examine this in some cases. You can entice the Warchief out of the citadel. For example, Khrosh metal-beard mostly appears near the border of the stronghold. Here you can try and use your charm ability to entice him out of the citadel.
6 Use the execute ability
Also, you can always try and use your execution ability wherever possible. The benefit of using it is that the Warchief's health goes down fast when used while attacking. The more executions you use, the faster you would be able to kill them.
7 Try to fight him alone
Another trick that can be used is when you see that there are no other arcs nearby then you can easily lure the Warchief and kill them quickly. (See How to do a strike from above in Shadow of Mordor?)
8 Focus on the Warchief
If you are in a situation where there are other orcs as well along with the Warcheif. Then, to kill the Warchief fast, you need to push the other orcs with a normal but keep your focus on the Warchief and target him with executions.
9 Fight at a high ground
If you have to attack inside the stronghold, you should try to lure the Warchief to high ground. The reason behind doing this is that it would become more comfortable for you to push the other orcs over the edge, and you can kill them with different strikes.
10 The most effective combo
One of the best combos is shock the warchief, strike 3 times, shock him again, hit 3 times, then execute. It would be best if you kept repeating this till the time you kill him.