I've never seen a DPS try to tank one of the sisters. One of the tanks usually holds Garuda and a sister and the other offtanks the other. MT with Garuda + Chirada and OT with Suparna seems to be the way that's had the most success for my groups. That way your MT doesn't eat two Wicked Wheels. Wicked Wheel is easy to detect as you'll see a target reticle be placed on a tank prior to it being used. Tanks just have to eat the damage, it's too large of an area to try to run out of. This is why melee have a lot of trouble in this fight because they have to anticipate when Wicked Wheel is coming.
The successful runs of this I've done has went as follows:
Phase 1:
Garuda tanked in the north part near the solitary rock. Hide behind frontmost rocks to the sides facing away from the middle of the area to dodge her line attack. Satin plume killed after jump then razor plumes killed. If DPS is high enough you won't get a second jump. If DPS is low, you get a second jump and have to hide behind the two easternmost rocks to dodge the line attack again and kill the plumes again.
Phase 2:
Sisters come out, ranged stay in middle. OT grabs Suparna and drags her to the southmost part of the arena with the MT tanking Garuda and Chirada in the original tanking spot. (The reason Suparna is grabbed by the OT is that if DPS is too low, the sisters will eventually do a jump and swap places and can potentially screw up the fight due to the confusion.) DPS focus down Suparna first while dodging the occasional Friction casts, then turn to Chirada. Once they are dead, Garuda will Aerial Blast shortly thereafter.
After Aerial Blast:
There's two phases that alternate post Aerial Blast.
Phase 3: Right after Aerial Blast Garuda summons razor plumes and a Spiny Plume. The Spiny Plume must not be killed until Garuda jumps in the air. Razor plumes need to be killed as they do considerable amount of damage. For the Spiny Plume, it puts a stacking debuff on people that need to be taken off of them after 2 stacks is reached. If a Spiny Plume aggros a non-tank you can just leave it on whoever it's on and then Provoke it off after 2 stacks are reached. If the OT has it they can trim down the health some with auto attacks. After Garuda jumps, everyone kills the Spiny Plume, waits until the red circle goes away, then jumps inside the area where the Spiny Plume died to survive Mistral Shriek.
Phase 4: Suparna and Chirada reappear with Garuda after she jumps after Mistral Shriek. Suparna is grabbed by the OT and tanked to the Western part of the arena. Chirada and Garuda are tanked towards the Southeastern part of the arena. DPS and healers (assuming all ranged) stand in the Southwestern part of the arena. If you have melee they will have to watch for Wicked Wheels. DPS follow the same kill order as before. (Suparna > Chirada > Garuda) There will also be a Spiny Plume in this phase that has to be bounced between the two tanks. The way to safely do this is you'll see a line that separates where the tornadoes form. Tanks can safely walk on these lines to avoid the tornado damage and run far enough to Provoke the Spiny Plume off of each other. Garuda will eventually jump, Spiny has to be killed as above, run into the area where Spiny died after the initial red circle goes away to survive Aerial Blast, and then Phase 3 repeats again.
At this point Phase 3 and Phase 4 will alternate until the boss is defeated. The groups I've usually run with usually take getting to Phase 4 the third time before Garuda is low enough to kill her. We usually utilize a caster LB3 to finish off Chirada once Suparna is dead and the OT has Spiny plume and trim down Garuda enough to finish her off.