I researched this quite a bit and there does not seem to be much on it
I did find the following which seems like the best advice:
Just finished Migraine with some buds, so I'll offer what info I learned. Goes without saying that you should bring the best food/util buffs you have, as well as repair cans since you will likely die a lot and you cannot re-enter by relogging like you can in fracs.
For Eir, we found it more useful to just dps Garm and save the CC for Eir, though if your group has excess CC or does better when you keep Garm stationary then go ahead and do what works best. Afaik Eir cannot be CC'd until she kneels to heal Garm so don't waste it while she's still running over to him. However, once her bar is broken she's stunned for a long while so use that time to dps like hell. Also, the speed mushrooms make it much easier to dodge her fire attack so remember to use those.
Canach put up less of a fight than I expected, the main thing is to stay mobile to dodge his various grenades and ranged attacks, and make sure to res allies when they're downed. As the article says CC is important to knock him out of his grenades-only phase quickly, don't bother with trying to hide behind Canach or shield yourself. Speed mushrooms are pretty useful here as well for dodging stuff.
Mordy is pretty similar to his fight in solo mode. It does some sort of retaliation/reflect attack that will throw a lot of confusion stacks on you if you're not careful; it's pretty manageable if you're using melee weapons but projectiles will reflect a lot more stacks onto you that can down you quickly if you're not careful. There is no visible buff on Mordy's buff bar when it does this but it does lean back and roar, and my friend using different graphics settings said she saw a purple ring effect around it. It always does this attack immediately after you turn Rytlock back to your side, there may be other concrete times but that's the only one I know of. As always remember to use speed and adrenaline shrooms, and if you have trouble getting up in the air during a flight phase remember that an updraft will always spawn on the friendly npcs.
In addition, during the last phase of the Mordy fight where you have to fight off the smaller adds, there is a repeating attack that will 100% down you if it hits. An aoe circle appears under you and the center will expand, you must dodge right before it meets the outside of the ring (can't confirm/deny if aegis/blocking works). Use the rift when you can (regular CC may work as well, can't confirm/deny since I was dead by this time and couldn't see well), then proceed as in solo mode.