I've run Garuda SM a bunch of times now and here are all the steps from my PLD perspective.
-- Tell your party to, except for one single time, never ever ever face Garuda. You may be able to absorb her slipstream attack if you end up getting caught in it and don't move out of it fast enough, but it can KO any of the others very easily.
-- Tank her to the most extreme far edge of the field as you can in phase 1. The way I do it is to just have her hugging the edge she starts on at first. When she respawns the second time and is on the other end of the field, I switch to tanking her on that side. Have her hug the edges because her AoE attacks will damage the stone pillars. You want the pillars as intact as possible for the phase 2 transition. The less of the pillars there are, the more damage your party takes, and it's extremely easy to wipe in the phase 2 transition.
-- When feathers spawn, they need to be destroyed ASAP. In phase 1, they attack the pillars to wear them down. In phase 2, they can harm the party. DPS and even the healer (if you use rampart and/or sentinel to keep Garuda from dealing you serious damage) need to nuke the feathers immediately, and if you can toss some shield lobs to the ones closest to you to help out, even better.
-- In phase 1, she respawns 4 times. The first, second and fourth times require hiding behind the pillars or else you die from massive AoE damage. The first time she respawns, it's right around where she starts off. The second time, it's right behind where the party starts off. Fourth time she respawns is in the center. When she respawns the third time, it's also in the center, but doesn't cause damage.
-- I would recommend having your party not touch the limit break and keep that just for you to use. The instant she disappears to respawn for the fourth time, I'd suggest using the limit break yourself to put up Mighty Guard for the party. If the pillars have been worn down enough, this will be the difference between surviving and a wipe.
-- That fourth respawn in the center is what triggers phase 2. The pillars are gone and Garuda shrinks the field down to a much smaller circle. This time, the barrier that surrounds you will damage you if you step into it. You need to stay within the barrier. Keep her facing away from the party, and you stay hugging the edge of the barrier as much as you can.
-- In phase 2, the first time she respawns, make sure everyone runs behind her. She does frontal AoE damage that will KO the party if they're caught in it. The feathers then reappear. Destroy them asap.
-- She'll respawn again after that, this time outside of the barrier. You and the party need to QUICKLY run as far to the opposite side from her as you possibly can. This is the ONLY time that you want to be directly facing her. Frankly, you have no choice but to face her, because there's no way to avoid it.
-- From here, she's at about 10-15% left. Nuke the crap out of her until she's dead. Use your buffs as needed to keep yourself alive for as long as possible in case your healer has died during any of the other hairy parts of phase 2. This means you should avoid using rampart and sentinel again once phase 2 starts until you're at this point. More than one Garuda run has ended with me ending up as the last man standing of the party, slashing the hell out of her like crazy while buffed and just barely killing her before I drop. It may end up being the same for you.
And that, sir, has been my Garuda experiences so far. With all of that being said, it's going to mean jack to you until you're actually running it and you start seeing the mechanics for themselves. Way easier said than done for the entire party. But when you get it down, it's an awesomely fun fight.