For anyone having trouble in the first phase and getting behind rocks when she teleports, you get a pretty large warning before she actually does it. If you are targeting her you will lose target a good second or so before she disappears, you can start running behind a rock immediately as you lose target then fine tune when she actually appears. You can even watch the mini-map to see where she is slightly before she appears too.

For the 2nd teleport + Mistral Song phase, there are tricks to how it works. She will either pop north/south/east/west or at the tank. If she pops at the edges of the arena you can run away from her to the very edge of the Tornado to avoid damage (once again, if you watch the mini map you get a good amount of warning). Your tank should be fighting her at the edge of the tornado so if she pops at the tank, they can run as soon as she disappears and she will reappear facing the wall still and won't hit anyone if you are gathering at the center when she teleports.

This fight just takes a lot of practice, efficient DPS (and gearing heavily for Accuracy), and smart use of combos. Our big breakthrough was not holding TP for AOEs and instead initiating combos on Garuda when she returned from Mistral Song/Shriek and closing the combo with AOE moves on clusters of Plumes after they spread out, with Bards picking up any stragglers. Doing it that way you still are able to AOE but also do extra damage to Garuda through the starter combos. We regularly do the fight with 1 WHM, 2 WAR, 2 BRD, 2 DRG (or 1 DRG 1 MNK), and 1 BLM and have no issues anymore getting past Aerial Blast. A WAR tank won't be necessary either once PLD gets fixed.