The big secret to a normal run would be to have everyone pop their AoE move the second the adds spawn at garuda, this way most adds will be almost dead without ever touching the stones. This goes for the tanks also (Circle of scorn for PLD, the wrath move for WAR).
Second tip is to not stand close to the pillars when Garuda moves to do a damage move, as long as you have a pillar between you and her, it wont damage you, but if you stand on top of it, the ranged attack she sends out straight after can hit the pillar and knock off a stone. Because of this you want to have some distance from the stones at all times.
As for speedruns (and youll do a lot of those once you're geared with relic), the most efficient way of killing her is the exact opposite. If you have enough dps, it's possible to have everyone only attack garuda, and ger her low enough to use Aerial Blast (special big move) before adds have enough time to do much dmg to the pillars. This is how people kill her in 4 min etc.
As for every other fight in the game, practice makes perfect, just do her enough time, and eventually you'll be able to predict her every move down to the second, just keep going at it, GL!
