1 Kill the guarding captains first
Each war chief usually has two captains who guard him. Identify those captains then before you begin the mission kill those captains.
2 Don't begin the mission with the captains alive
If you began the mission with the captains alive it might be hard to kill all of them together.
3 Identify guarding captains from the army screen
Go to the army screen and click on the Warchief you want to kill. You will find two lines coming out of the Warchief and pointing towards the captains who guard him.
4 Finish the captain related missions first
For each captain there is usually a mission that can allow you to kill that captain easily in a relatively isolated area.
5 Lure the warchief out of the stronghold
In some cases it might be possible to lure the Warchief out of the stronghold, for example Khrosh metal-beard usually appears near the border of the stronghold. Use your 'attract' ability to lure him out of the stronghold.
6 Use the execute ability
Use the execute ability whenever you can. When you use it to attack a Warchief his health will go down fast. The more you manage to do those executions the faster you will manage to kill him. See how to do executions.
7 Try to fight him alone
If its possible to lure the Warchief in an area where no other orcs are nearby then you will easily be able to kill him.
8 Focus on the Warchief
In case you had to fight the Warchief along many other orcs then focus on the Warchief to kill him fast. Push away the other orcs with normal hits but always target the Warchief with the executions.
9 Fight at a high ground
If you have to fight inside the stronghold then lure the Warchief to high ground. In such a case you will easily be able to push the other orcs over the edge and so kill them with few strikes. See how to do the critical near death strike.
10 The most effective combo
The most effective combo is as follows, shock the warchief , strike 3 times , shock him again, strike 3 times then execute. Keep repeating until you kill him.