Branching off the other solutions, I would like to explain and elaborate why it's not intelligent to readily dismiss Death Threats when working towards this achievement.
Apparently, issuing Death Threats only SLIGHTLY increases (by 40%) the chance of a targeted Uruk to drop an Epic Rune. The other solution mentions to ignore Death Threats and work on exploiting a Warchief's fear, but none of the starting Warchiefs in this DLC have weakness to exploit for that +1 Rune point, and why are we going to waste time grooming a Captain? Fret not, gamers.
When the Trial starts, head to one of the several Power Struggle missions and fight the Captain there. Dominate him at the end and reveal the identity of a Warchief (it doesn't matter which one, but I like Tumhorn, the poison arrow, bow wielding, ugly faced Uruk). Once that Warchief's mission appears in the world, head there, start it, complete the prerequisite to lure him out…then allow him to kill you. Make sure the Warchief gets the finishing blow on you!
When you spawn at the Forge Tower, go ahead and find another Captain (be it through Power Struggle missions or free roaming the region with Wraith Vision enabled) and dominate him however you see fit. While holding this Captain, do not worry about gaining intel, ISSUE A DEATH THREAT to the Warchief that just killed you.
Now go to Sauron's Army screen and you'll notice that because the Warchief killed you earlier, he'll have at least one bodyguard (or two maybe,). It's worth noting that initially, these five Warchiefs do not have any bodyguards. Upon killing you however, they will sometimes obtain one or two (and in some cases, none at all!). If they do have a bodyguard, find one of their identities through worms, intel or other Captains around the region. When you go to track down the bodyguard(s), do what it takes to DOMINATE them, then DISMISS them. DO NOT KILL THEM.
Once that's through, go back to the "Unfinished Business" mission from the Warchief who is savoring in your defeat. Start the mission up and he'll show with his bodyguards (whom you have branded) and a small gang of Uruk grunts.
Initiate the fight against your foe and do what you must to get as many Uruk Grunts dominated under your control. Obviously, Wraith Flash Domination (X+A) works best to dominate several Uruk at once.
The Warchief's bodyguards and now all the Grunts will be attacking him like crazy. Get some executions and stuns on the Warchief if you want to speed things up, but DO NOT deliver the finishing blow!!! Jesus, DON'T DO IT!!!
When his health is really low, allow one of your several dominated Uruk allies to deliver the finishing blow and the Warchief will drop a Level 30 Rune - NOT an Epic.
I tried this out just now
FIVE TIMES back to back to back to make sure it works consistently, and it does.
This method is super easy because you don't have to go through the trouble of finding that ONE single Captain who has an easy fear to exploit and waste time leveling him up and getting him to become a Warchief. No offense to the other solutions (which are great), but it's more time consuming to find an exploitable Captain and level him up and all that jazz. This method detailed above works within the first 10-15 minutes of the Trial.
For those unfamiliar with how this Warchief is dropping a Level 30 Rune, let me break it down: A Greater Uruk (Captain or Warchief), when killed, will drop a Rune of HIS current Level. There are 5-6 additional points that can be added to his Rune. If you haven't already guessed it, Level 25 enemies are the highest enemies in this DLC Trial.
The Warchief, already being a Level 25, will net +2 points to the Rune since the status of being a Warchief grants +2 points.
Since he killed you and is now a revenge target, that's +1 point as well.
Issuing the Death Threat yields another +1 point.
And of course, since you know his identity and his strengths/weakness from interrogating that Captain in the beginning, that's another +1 point.
It's worth reinstating that issuing the Death Threat DOES WORK - please do not let people's comments that state otherwise confuse you or deter you from thinking what's correct - but you CANNOT be the one to deliver the final blow. Your allies MUST.
For a visual representation of how all this plays out, go ahead and check out the video below, courtesy of Chaotic Fiasco.