In both of these fights, Holy helps a lot.

For Garuda (I'm assuming normal mode?), after she teleports and you hide behind the rocks, run up near her, turn on Cleric Stance, use Swiftcast (optional, if you have it), then Holy when the feathers appear, turn Cleric off and back to healing. Also, stay spread out on the outside edge. Friction really hurts on NM, and you don't want it to hit more than one person at a time if you can help it. After she destroys the rocks (The Reckoning Comes), get everyone healed back up with some medicas, but make sure you always stay focused on the tank first. For the second half in the middle, always stay behind Garuda or as far away as you can. Don't be afraid to use healer limit break if you need to.

For final boss in Aurum Vale, the key point is using Holy on the seeds before they ... spawn/hatch? Also really need the tank to dodge Bad Breath. If they do get hit, don't bother trying to esuna it all. Takes too long and too much mp. Don't forget to eat fruit at 3+ stacks.