Basic strategy - This is actually an easy area to complete provided you have about 10 people and maybe a summoner in the alliance for a carbuncle pull at the end when it's time to fight the two Light Elements and Mystic Avatar. The first thing you gotta be aware of is that each time you kill a regular Elemental, the Elemental who's element is weak to that Elemental that you just killed with change to a Mystic Avatar that can and will use Astral Flow. Of course you don't really want to fight a bunch of Mystic Avatars that can Astral Flow your alliance. Add into the fact that you really can't stun Astral Flow too. At any rate the best strategy is to reduce the number of Mystic Avatar that you need to fight to just one. This can easily be done by fighting the Elements in certain order. But to cut through the chase here's the order you need
to fight and kill these Elementals. Kill the Water Elemental first than the Thunder Elemental follow by the Earth Elemental than the Air Elemental than the Ice Elemental and finally the Fire Elemental will turn into a Mystic Avatar (Ifrit). Fighting Ifrit is really the best choice as Ifrit is a pretty harmless Mystic Avatar. Just remember that when moving around from one Elemental to the next, try to stick to the walls so you don't accidentally aggro the Carbuncle Mystic Avatar and his two Light Elemental buddies.
Okay now that you've manage to get rid of all the regular Elementals, it's time to pull Carbuncle Mystic Avatar and the two Light Elementals. Of course the best way to do it is to the your Summoner Carbuncle pull each of the Light Elementals one by one and taking them out. Once they are gone you can just concentrate on Carbuncle Mystic Avatar making things very easy. Of course if you don't have a Summoner than you'll probably have to sleepga II the two Light Elementals and take out Carbuncle Mystic Avatar as quickly and as best you can ignore the two Light Elementals till the Mystic Avatar is dead. You can't sleep Carbuncle Mystic Avatar at all so best to take that one out first and quickly if you don't have a Summoner to pet pull the two Light Elementals.