Garuda's damage are physical, so her attacks are ruled by physical (not melee) accuracy cap, for example if you try to auto-attack with your smn/blm, you'll have some misses until you're capped !
Btw the Bard is ruled by front/flank/back accuracy rules, and it's probably the same with garuda, so try to keep her at the back of the boss and you'll probably miss less.

Oh, and do you know if she only misses her "basic attacks" or her Contagion can miss too?