After many, many attempts at 40 minutes a pop, I have finally done this. Thank you all for your input in the comments section as it really did give me, and i'm sure others, new strategies to work with. I've done this 5 consecutive times now, I know this method works. If you are struggling with it and find it isn't for you, I would suggest trying one of the other excellent and very well detailed guides below.
NEW video guide on Youtube. You'll see in the video I do this in 36:22; my best time yet, i even made more than a few cock ups (as usual, running into walls, warchief essentially suffering a heart attack etc) so there is more than enough time, points aren't great, but as i've always maintained, I am playing for the achievements (and in this case helping you guys get it) and I couldn't care less if I am at the top or the bottom of the leaderboard and if you don't either then please watch and enjoy.
Essentially for this achievement you must complete the Test of the Wild whilst completing the main objective, plus all 3 bonus objectives.
These are as follows (although note, possibly not verbatim):
Main Objective: Kill all 5 War Chiefs and all 20 Captains
Bonus Objectives: Complete the challenge in under 40 minutes (bonus 1000 points)
Kill 10 Captains using a beast (War Chiefs do not count)
Obtain 13,000 points (12,000 plus above bonus)
Now this is by far the most challenging achievement in this game. You will likely attempt this and fail several times and get very frustrated (I know I did). It is very much down to luck of the draw, specifically in terms of enemy placement but perseverance is key. You cannot afford to make mistakes and I cannot stress enough the importance of using the map and the Sauron's Army page to your advantage-it wastes too much time to go to one area of the map, kill a few captains, race to the other side of the map and then realise that there was another one in the area you were previously. Furthermore, you cannot let enemies escape, that also wastes too much time as you are essentially having to track them down and battle them twice. You will want to spam use of LB (think it's called wraith vision or something) to pinpoint your foes in these areas.
When you start, immediately drop down and start dominating the generic uruks until you have intel on all 20 captains. If you happen to see worms or intel pages by all means grab them to use on the war chiefs but don't worry too much about the war chiefs for now. Now, ignoring any involved in power struggles, the majority of the captains will be centered around the 3 strongholds; the shanty town type area in the south, the fortress to the north-east and the fishery to the north-west. Use the Graugr bait on the nearest NORTH-SOUTH facing bridge to where you spawned (there is an East-West facing one not too far away) and mount the Graug using shadow mount and using the Sauron's Army screen track all the captain's down using the Graug's Y button move to bite their heads off, killing them in one hit. Ensure that you have killed every captain in that area before moving onto the next one. Again use the Sauron's Army screen to your advantage to mop up any captains not in the strongholds as you traverse the map from point to point. If you think you may have messed up and lost a bit of time, you can also ignore any Uruks who you know are bodyguards (as you can kill them during the War Chief fight), although it's probably safer to just kill all the captains (again, to clarify NOT those involved in power struggles), before moving onto the War Chiefs. You should have more than 10 beast kills by this point so that's one objective down.
With all that done I would suggest having at least 10-12 minutes left on the clock and as ever expediency is still a must. I would 100% recommend using Ugakuga Graug Rider (he doesn't actually ride a Graug like he does in the story) as the War chief to dominate, as a beserker class enemy he has a move where he can trip enemies up and then do a one hit kill move (it's actually 3 or 4 hits in the animation), where he just lays into them while they are led on the ground. This is particularly useful against Shagflak Ghul Keeper who is all but invincible to anything you can do to him unless you have a Graug handy but can seemingly be harmed by other Orcs regardless. Even then he's still a bit of a hard case but in the 4 times him and Ugakuga have gone toe-to-toe for me, Ugakuga has come out on top. Ugakuga is also pretty easy to beat as you can use the stun move or the move where you jump over him and then use combo flurry until you have a finisher, use both finishers on him, rinse and repeat. The only potential problem is that he never turns green, meaning you can't actually garb him but every time for me he has done the thing where he drops to his knees on low health and you can either kill or dominate him (i'm not actually sure what let's some captains and war chiefs do this when others get killed outright). Regardless, once you have dominated your warchief, command him to riot against each other warchief and any remaining captains (the 3 or 4 who were involved in power struggles). Utilising Riots not only skips out the mission to draw out the warchief but you also have a load of friendly uruks should things get too hairy. I would always advise killing all of the war chief's/captain's troops first and then killing the leader apart from in the case of Tumhorn who can be killed instantly with a stealth kill and will likely be alerted if you start shooting his troops. Zugor can be a pain with his rapid firing exploding crossbow but building up combo chains whilst killing his supporters and then using flame arrows on him makes short work of him as he is distracted by your uruks.
Truth be told the only captain or war chief who is consistently a nuisance, is Shagflak who I mentioned above-he will likely take a good 1-2 minutes for your guys to kill as they are pretty dumb and you can't do anything to help.
Now the question of points. DO NOT DISPATCH YOUR DOMINATED WAR CHIEF (who should be the last target standing) UNTIL YOU HAVE AT LEAST 12,000 POINTS! I never had a problem with points (you can see I'm currently 4th on the world leaderboard for a narrowly failed attempt)-except on the time I actually did it. I was over 1000 points short after killing my last target (excluding my dominated war chief obviously) and with only 90 or so seconds left I started panicking. Now in the wake of the last riot there were a lot of dominated uruks stood around who I built up combos on and then used finishers to build up some half decent points. What really did it for me though was killing 3 Carragors for I think 105 points a pop. That was luck as if they hadn't been there I likely wouldn't have got the points in time. To remedy this I would suggest making sure to kill your Graug once you are done with him and if you get an opportunity to kill Carragors (a lot seem to spawn around the starting area where you will be dominating uruks for intel) for a tidy point boost (the clock also stops whilst in focus mode-this can be used to your advantage to cover ground quickly as well). Ultimately you will also get points for dispatching your own war chief but I can't imagine this is more than 1-200 so I would play it safe. Provided you have done it in under 40 minutes you will now get a 1000 point bonus to take you up to 13,000+. Congratulations.
This challenge is annoying, it will take a lot of time and effort and ultimately I barely made it by the skin of my teeth (I am currently sat at the bottom of the elite leaderboard and had a measly 25 seconds left before failure), but as someone who has been devoting all my gaming time to this since it was released and thought it impossible, I can now say it is doable but very challenging.
Good luck doing it, please let me know if you've found any other helpful shorcuts or methods and remember: ALL HAIL BASED UGAKUGA.
EDIT: I just did this for a second time. I was streaming via Twitch but being my first time and with Twitch never mentioning that you have to select a box in settings to make videos archive automatically, it hasn't saved. I actually completed it again with just over 3 minutes to spare and this time had a comfortable amount of points. I even died twice whilst doing it. The more you try this the easier it gets, evidently.