Trixie, Mixie and Dixie.
Pull them one at a time, burn them to 5% or less (do not kill them yet). Trixie is a healer (collector of faith) and she heal herself over the course of the fight. Burn the other two first, then pull Trixie. When it gets to 5%, carry on burning and go nuts on AEs so all die within a few seconds of each other. If not the encounter resets if they are not killed within 5 seconds of eachother.
The sub-names have differing health values so plan your pulls accordingly.
When Elaani comes, get all but tanks at max range (30m+) as she has a big proximity AE on incoming. You will have time to get out as she has a dialog box or two before she comes after you. BladeDance helps a lot when Elaani is on her way. Burn her adds and then the Named.
Good Luck.