In my experience, Warriors make the best main tanks on Turn 5 due to the availability of Inner Beast for every Death Sentence, whereas Paladins' cooldowns may see them lacking towards the later phases, which is why I am surprised to see you say that you've rarely main tanked the fight.
As the guys have said in previous posts, keep Storms Path up at all times - Alternate between Butchers Block and Storms Path combos, and ensure that you have Inner Beast up for Death Sentence. In the first phase, she will do two Plummets between Death Sentence, so when you receive that second Plummet, hold off on your attacks (providing you have enough Wrath Stacks, if not > Infuriate), and pop Inner Beast as soon as you see the cast bar for Death Sentence. This is how I used to have to do it pre-Echo Buff and it used to work at ~iLvl85.
One thing I've noticed since 2.2 is that a lot of Tanks also no longer go into the Conflags while they are up. By doing so, you can completely avoid all Death Sentences during this phase if the timings are sync'd up correctly. Healers should be keeping Regen on you and providing you have over 70% HP, I would recommend doing this, as it also gives the Healers a bit of a break. I still do it now, even at iLvl96.
Once you reach the Twister phase, you will be tanking Twintania while the Paladin OT is on Dreadknight duty with stuns. During this phase she will be doing Twisters as well as Death Sentences, and the best way to avoid Twisters is to run in a circle underneath the middle of her, so that she does not move from her spot, and that you avoid being hit by any melee's Twisters, and that they avoid getting hit by yours. Again, ensure that Storms Path is up at all times, and use Inner Beast for every Death Sentence. Timings can become skewed due to her attacks queuing up behind one another, but you will still always have enough time to build up five stacks of Wrath.
During the final phase, she will cast two sets of Liquid Hells between Death Sentences, so again you can use the second set of Liquid Hells as your indication of incoming Death Sentences.
If you are doing everything correctly and following these guidelines throughout all these replies, and still dying, then you need to start questioning your Healers, as they should be doing everything they can with Stoneskins and Adloquiums to help you mitigate Death Sentence. If they are too busy to do this every time, and you have a Paladin OT, ask him to cast Stoneskin on you for each Death Sentence as well.
As for Garuda XM, unless you are running double Warrior, Paladin is usually the better choice for main tanking due to their more expansive cooldown suite and raw mitigation through Shield Oath. Timings for WW can become skewed depending on DPS, but Garuda and Suparna will often jump before they do it, so if you are main tanking, while they are gone and while avoiding Featherrain, pop a cooldown and hit one of them with Inner Beast as soon as they are targetable again. White Mages should also be putting Stoneskin on you during the time they are gone.
Hope this helps ^^