I was the 2nd person to unlock this achievement :)
As soon as you start, lean over the edge and shadow mount a caragor. Press LB to put on your ghost vision and look around for Captains, sometimes there's one or two right by where you start. If there's Captains kill them but if not just start riding around turning your ghost vision on and off looking for them. After playing a bunch you should be familiar with the areas which Captains hang out and you can ride your caragor around trying to find them saving time by using the new slow down time feature for your caragors from the new DLC (Jumping over rocks and coming down from ledges will prompt you to press A and you will run faster and the time will slow down. You must utilize this as much as possible.) While looking for Captains, if you come across some easy to get intel go and grab him and unlock some Warchiefs.
The first thing you want to work on and get out of the way is the 10 monster kills. Even though grabbing graugs and running into forts to eat Captains is good and you can try do this if it works out for you especially in the top left fort and the bottom middle are pretty easy to run through places with the graug and you can get some easy monster kills on the Captains. During my run that I got the achievement I barely even used graugs, only once or twice. The way I was getting monster kills was running around with the caragor and trying to stealth kill Captains, sometimes they would die instantly. If they didn't die I would shoot them with arrows until they did, which counts as a monster kill fortunately. If the Captain was unable to be hurt with the ranged attacks/arrows I would hit him with the sword trying to kill him and when he had low health you can hold RT and press Y to jump off your mount and assassinate him, which also counts as a monster kill. If you try to eat the Captain while hes on the ground it usually doesn't do much damage or he could kill your caragor so I would refrain from that. If the Captain causes too much trouble or kills your beast you can just kill him and move on or you can look for a graug spawning bag of rocks (which are hanging around various spots on the map) you can see them when you turn your ghost vision on.
So get the monster kills on Captains asap and grab intel so that you can unlock Warchiefs. The Warchief that you need unlocked is the big one, the berserker Ugakuga the graug tamer. Hes the only Warchief you need to unlock. Once you've got your 10 monster kills and unlocked the graug tamer with intel go and start the mission to call him out. This should be your only mission you do to call out a Warchief since they take up too much time. Do the objective, once hes out try to kill his bodyguards first if he has any, then beat his ass. Don't kill the Warchief but dominate him and command him to riot against another Warchief. Go to the riot mission and kill the Warchief and make sure your dominated guy stays alive. I tried to kill the Warchief first mostly because when a Warchief dies one of his bodyguards will take his place and you can kill him right there after and you will be rewarded with more points for killing a Warchief rather a Captain. The only thing is the bodyguards will be running away after you kill the Warchief so you gotta be quick.
Now once everyone is dead, grab your dominated Warchief before he vanishes and dominate him again and command him to riot against another Warchief. This is what you're gonna be doing for the rest of time. Commanding your Warchief to riot saves you so much time because you don't have to waste time drawing any Warchiefs out, you just go to the riot mission and try to kill the Warchief as fast as possible. (Just make sure your dominated Warchief doesn't die or escape while doing the riots) Going to a spawn tower and pressing Y will "Advance Time" and by doing so you can turn the other Captains (unknown or not) into Warchiefs and continue to riot against them with your dominated Warchief. Doing this you will have no problem getting under the time limit. The only problem you might have is killing some of the Warchiefs. One of the Warchiefs you can kill with a stealth takedown but some of the others are tricky. For the Warchief with the crazy rocket arrow shooter, the beast killer I believe, you can kill him with Shadow Strikes. Just spam him with it by holding LT and pressing X, don't even give him a chance. Shagflak the grul tamer Warchief basically can't be hurt by your attacks, but you can combat drain his guys and they will attack him and kill him or you can grab a graug if theres one close by.
Now for the points, which was my only problem after using dominating and riot technique. The best way to make extra points in my opinion is executing controlled monsters. Towards the end I was coming up short in points so I was shadow mounting caragors and graugs and then killing them by holding RT and then hitting B (I think) to kill. It gives you 150 for a caragor and 200 for a graug. If you kill your tamed monsters while your going through your 40 minute run you should have no problem with the points. I didn't start killing my beasts until my last 10 minutes. Well good luck with this achievement and I hope this helps you, please feel free to ask me any questions.