I've finished all 3, waiting for more NA people to get out there with me so I can start up the next section - Phomiuna Aqueducts...
The strategies for the boss fights kinda vary with what you can get. Promyvion - Dem is the most lenient on what kind of group you have, but the main thing throughout all of them is that you have to give yourself a minimum for damage dealer potential.
Rangers and Summoners are the best classes to have with you, but you don't always 'need' them in 'your' party depending on the Promyvion you're doing (see above). Try to get at least one blink tank (preferrably Warrior for the better two-hour ability) but always get 2 tanks, since these bosses hit hard, and you don't want your healers to run out of mana too quickly.
Some people will kite the boss, but in every fight I've won, we just straight out tanked it. Don't discount having a BST come along if you have someone who wants to come since Courrier Carrie can actually do some more damage than a War/Nin, and then you have another backup healer and melee in one. I actually beat the Holla boss with a BST in the party.
The biggest things to worry about are making sure everyone brings some appropriate items for the BCNM you are doing (I won't go into it, as I'm linking other people's posts, haven't decided if I want to be redundant and make another 'how-to' of promyvion) and finding people who all have 2-4 hours of time they can stay logged on. If you're in a good group, you can get through a promyvion in 1 hour after getting the alliance formed. A bad group will take 4 hours after it's formed, and that's if you can get passed the third floor without someone getting killed.
One last thing before I finish: try to grab a small prep-group together and farm up recollections (not the remnants of memory). You make Animas from a quest with these that can help you finish off the bosses (just don't use them too early in the fight or you'll make it worse for yourself).
There are a few strategies floating around the Mission and General boards:
Promyvion BCNM battle strategy Promyvion-Mea Boss Strategy Seems like a nice general strategy, but no real boss info other than the anima effects strewn throughout the thread:
How to beat promyvion.
This is the thread I got all my info from when I was doing the Promyvions:
Promyvion - The Emptiness - Get your game on Just to give you some ideas, I'll list the group types I've won with:
DEM - WHM/BLM (me), WHM/BLM, BLM/WHM, BLM/WHM, WAR/NIN, WAR/NIN
HOLLA - SMN/WHM (me), SMN/WHM, BST/WHM, RNG/NIN, WAR/NIN, WAR/NIN
MEA - SMN/WHM (me), WHM/BLM, PLD/WAR, WAR/NIN, RNG/NIN, RNG/NIN
Hope that helps some, now will someone get out here and help me out?! *cries*