The Hoot of the Issue

FORENOTE: as stated by other people here, this achievement is still bugged. Alderyn and Myn'ir victory is counted but Splinterbark Nightmare is not. Won twice just to check as I'd not been to check on here beforehand, but nope, still bugged. Wouldn't recommend bothering till it gets fixed sadly.

Can now confirm this achievement has been fixed and can now be obtained, as others here have mentioned!

(But did have an issue with the splinterbark nightmare boss resetting once, also as mentioned by others here- may have been a bug when Mikanikos is dispatched and doesnt take aggro but not sure)

Here are the tactics and tips I went with for approaching these encounters-

Alderyn & Myn'ir
Myn'ir

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• Dodge Myn'ir's arrows as best you can, but otherwise, ignore her. The shared health pool means only 1 needs damaging and trying to cleave them isnt really practical.
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Alderyn

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• Interrupt Anima seed with the Deep echo trident. you wont be able to interrupt every one, but it saves you some trouble. not worth interrupting his other casts.
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• Focus on standing in the anima seed and dodging the arrows and wind when the anima seed gets cast.
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• Melee him whenever he is in range, but dont focus on it. the melee ability is mostly useful for springing up energy orbs to collect, so you can recharge for the big beam attack.
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• Use the big laser beam attack on him as often as you can, without going too low on energy.
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This fight was tricky for me but I had steady progress learning it- my win occurred on my first attempt with charms- but I think with more practice I would've gotten it without. Working on this boss was also my first time playing with Mikanikos and Bron, so it was quite fun to learn the team mechanics.
The equipment here does not necessarily need to be the Deep Echo Trident as Alderyn will cast at times when the Trident is still on cooldown and you'll just have to go soak a seed anyways, but I found it helped a lot.

Splinterbark Nightmare

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• Keep moving- it is the best way of keeping out of the splinters that the boss drops as the swirl indicators can be tricky to see under Bron's big feet.
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• Grab the green swirlies with flowers- these give a stacking damage reduction buff up to 90% at 10 stacks
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• Aim to have 10 stacks of damage reduction when the boss goes into enrage mode (this occurs when the boss reaches 100 energy). The buff lasts about 15 seconds, so picking up that final stack right as he enrages means you will have maximum duration.
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• Use spirit forged aegis equipment to tank the duration of the enrage. When enraged, the boss will use a cast attack when in melee range which reduces his energy by 10 each time; if you cast the aegis just as the casts his first attack the damage reduction buff and aegis make you basically immune until he de enrages.
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• If things don't go to plan Bron takes more damage than can be managed, so his self heal is needed. the initial phase of collecting the defensive buff also means Bron will take some damage before he is properly protected so it may be needed anyways, so take this into account when keeping an eye on your energy.
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This fight felt easier than A&M for me, mostly due to basically cheesing it by dropping Mikanikos at 0 health and polehumping the boss to get abilities off cooldown. What I've put above is my ideal method, but again, things rarely go to plan. By cheesing, I mean taking advantage of the fact that if Bron dies but still has energy left, Mikanikos can go collect energy orbs and return to Bron with energy and health at an equal % to current energy (I think- this may or may not be a bug).

This meant that if I failed on the defensive buff collection stage, I would take as many hits as possible with the aegis on Bron, then put on a few hits to spawn some orbs before Bron gets clubbed to death. At that point it would be speed buffed Mikanikos collecting orbs, and then kiting the boss around a pillar in the arena until the sprint and defensive were back off cooldown. This time wasting strategy meant that by the time Mikanikos got back to Bron, the spiritforged aegis was back off cooldown as well, and Bron could tank a few more blows to get the boss to use energy. Without the defensive buff, the aegis can take 3 hits before it breaks, so in the event that I failed to get the defensive I would have to repeat this 3 times. Sometimes, Mikanikos can take a hit if his defensive is up and he has the tail end of a few stacks of the green flower defensive buff still.

Charms
For the Alderyn and Myn'ir fight that I won I used charms of Focus, Persistence and Quickness. I didn't use them on Splinterbark Nightmare.
The resource and health regen both affect Bron even when not controlled.
Charms are a bit of an effort to craft, so while you are learning the fight, its better not to bother with them until you think you can manage. I gave them a go when i was managing to get A&M down to 40k ish health or less a few times in a row.

Mikanikos & Bron

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• For A&M I tried to avoid using the heal due to the drain on energy and the mostly avoidable damage- in a pinch it is helpful, especially as dodging stuff is hard with how big and slow Bron is, but it is energy better used for beam attacks. I also avoided throwing Mikanikos as much as possible for the fight; though he is fast and able to grab energy orbs and return pretty quickly, i usually came across 2 hurdles- while Bron appears invincible when not controlled, particularly on A&M, Myn'ir focuses her arrows on him for some reason when Mikanikos is out, meaning hopping back in often means there is some very hard to avoid damage in store
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• For Splinterbark Nightmare I did a lot more throwing Mikanikos, taking advantage of the immunity Bron has in that time and also using it to kite the boss for some distance so abilities could recover. I think by this point I was also more familiar with the abilities at my disposal as well, which may be why it seemed easier.
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Comment is a bit long, but hope it helps!

I have created video guides for this fight for when it is no longer bugged on splinterbark

Alderyn and Myn'ir with Mikanikos on Loyalty
https://www.youtube.com/watch?v=HLoR1g1bgVY

SplinterBark Nightmare with Mikanikos on Loyalty
https://www.youtube.com/watch?v=plu2fiHg4uQ

Just got the achievement as of 4:38AM 5/2/21 on Ravencrest so I tentatively suggest it might have been fixed.