This will likely be the hardest achievement in the dlc, but take comfort in knowing that it's much, much easier than the Test of the Wild. That said, you're still going to need a little luck, but knowledge and skills play a much larger role this time around.
For starters you'll need to remember that Celembrior plays a bit different than Talion as well as how he did in the dlc's campaign. Thankfully he's more like Talion in Test of the Ring, but he does have differences you need to note.
For starters when Celembrior aims his bow he does not get Focus, meaning time will not slow down while aiming. To compensate he doesn't need to charge his arrows, so each one shot will always be fully charged automatically. He also gets access to Shadow Brand (
), a move like Shadow Strike except it uses three elf-shot instead of two and brands the target. Like Shadow Strike, Shadow Brand can be chained to other uruks.
Secondly, Celembrior can summon five branded uruks to fight for him by pressing
. This can also summon branded captains as one of the five if they are nearby. He gets health when you use Consume (
). However, Consume WILL NOT KILL branded captains or war chiefs. This is very important, because Celembrior can't issue commands to branded captains and war chiefs. This means you can't start murders or riots, meaning you have NO reason to brand war chiefs in this trial. If you do brand a chief, you'll need to kill him by beating on him, since you can't use Consume. This will waste valuable time, so don't brand war chiefs.
Edit: As The Allslayer stated in the comments you can dominate, interrogate, and then kill war chiefs. This can help aid in gathering information. Just be very, very careful to select kill after interrogating if you chose to do this.
Thirdly, where Talion had three special meters he could fill for stealth, bow, and executions Celembrior has one. This is The One Ring, which combines all three abilities into one. Thus you'll have infinite fire arrows, executions, and become invisible when you use it. It also has the added bonus of negating the immunities of captains when used. To charge it up you'll need to dominate uruks. Any action that can brand works, so you'll have a lot of options. Branding caragors and graugs will also fill it.
By understanding Celembrior's abilities you'll have a much easier time with the challenges. The main goal of the challenge will be to kill 5 war chiefs and 12 captains. You don't need to worry about having them dead all at once thankfully. I killed one war chief and then took a No Chance arrow to the face. A branded captain filled the vacant spot, but even though five war chiefs were in power my tally still showed 1/5 war chiefs killed. Thus you just need to get the total needed number of kills.
You'll have three bonuses you'll need to meet. You'll need to brand a combination of eight captains and war chiefs, brand 50 grunts (any non captain uruk counts), and finish in 60 minutes. Remember that Celembrior can't kill captains and up with Consume, so don't brand the war chiefs, as you'll need to kill all five for the main objective. You'll have 20 captains running around, which should give you enough for the eight brands and 12 kills that you will need. Be mindful that you need eight branded captains/war chiefs at the end. You can't brand and then kill something, as that will only count towards a kill for the respective class.
Branding the 50 grunts will be done as you progress through the trial. You'll be branding to help refill The One Ring, and you'll likely brand quite a few to act as meat shields while dealing with captains. I would advise making use of Wraith Flash (
when combo meter is red). When fighting captains, especially in forts and strongholds, you'll have a lot of uruks around. Two Wraith Flashes used back to back can convert a lot, which helps add to your total and creates more distractions, making it easier to deal with captains. In short, don't be to concerned about this objective, as you'll likely hit it with ease.
The 60 minute time limit is again the hardest condition, as you're going to feel pressured because of the clock. Still, you're going to have a lot more breathing room than in you did in Test of the Wild. Be mindful of it, but focus on kill/branding captains and war chiefs.
The trial itself is fairly straightforward. The map is smaller, and captains are much easier to find then they were in Test of the Wild. Be mindful that they are much stronger though, as they'll have power levels of 21+. You won't be able to take much punishment, so be mindful of their attacks.
Like in Test of the Wild your time stops while looking at the map and Sauron's army. You're going to want to get the intel on the war chiefs as soon as you can. Since you can't start riots you'll need to flush them out via their missions and you need to know what those are. Some will take very little time while others will take more. You need to know what you'll have to do so you can budget your time. War chiefs will not start with bodyguards, from my experience, so unless you die or fast forward time you should only have to deal with them you go for the kill.
When you go to kill a war chief always go with a full The One Ring bar. Once you flushed them out use it. I only used executions, and was able to kill Tumhorn, Skak, and Rug before it wore off while leaving Gorfe and Akoth near death. I completely forgot about fire arrows, so you may want to try spamming those instead, but it shows that fighting with The One Ring available makes the war chiefs cake. Keep in mind that all starting war chiefs will be vulnerable to combat finishers, so you can make use of those if you don't kill them when using your special.
Once you kill one war chief go off and kill/brand captains until you fill The One Ring again. Dominating uruks will also help towards your brand 50 grunts objective. Once it's filled go kill another war chief. Be mindful when attacking though, as you can run into captains while fighting the chief. The One Ring helps mitigate this a bit, as you can focus and kill the chief and then work on the captain, but if you can kill the captains in a fort/stronghold prior to starting a war chief mission you're highly encouraged to do so.
You're going to be going after captain's quickly, as speed is key. If you see one in a fort or country side kill him. I'd recommend beating him until he gets the green circle and then grabbing with
and dominating with
. Immediately grill him for information and revel a war chief, if you're missing them, or another captain if you've got all five already. Once done kill him or brand him. Keep in mind that you only need 8 captains branded and you can't kill them with Consume so try to balance your action between the dominating and murdering. If you notice any power struggles involving two captains, like an execution or duel, take advantage of it.
Finally, you may find yourself coming up short depending on how things have gone. I had one war chief left, with one branded war chief (I died and the captain was promoted) and six brand captains. I needed one more captain kill and one more brand, but I had no more captains, and fast forwarding time wasn't bringing in any replacements. If this happens to you simply find a group of uruks and let them kill you. This will promote one to captain. I had to do it twice on my successful run, so be mindful that you can do this if you're coming up short.
That's about it ladies and gents. You'll still need a little luck, and you may have to try the challenge a few times. Since you've had the patience to read to the bottom of this you undoubtedly have the patience to clear this trial. Give it a go, learn from your successes and failures, and before you know it you'll have another achievement to add to your collection.