With Cid's airship outfitted to get past the barrier in the Howling Eye, you go to face Garuda.
How to Unlock
The Howling Eye trial is unlocked by the level 44 Main Scenario Quest Lady of the Vortex.
The tank should turn Garuda to face north. The rocks in the middle of the area need to be protected from damage, because players will need to hide behind them to avoid some attacks. The tank should move Garuda away from those rocks, and all players should avoid standing near them until they need to be used as a shield.
Garuda will periodically cast Friction, which targets a single player and causes a circle of damage around them that can hit the rocks and other players if they are close to them; Downburst, which is a large cone; and Wicked Wheel, a large circle attack around her. She will sometimes cast Slipstream, an interruptable cast. If it is not interrupted, those hit by it will be stunned. It hits in a straight line, so players can sidestep while she is casting it to avoid it.
After she receives enough damage, she will fly up into the air, then will reappear and cast Mistral Song. Players can avoid damage by hiding behind the rocks in the area.
She will later summon several Razor Plumes, which will fly to the rocks in the area, and after a while they will self destruct, damaging the rocks. Destroy as many of the plumes as you can before this happens.
Eventually, she will cast Aerial Blast, destroying the rocks. A purple swirl will surround the area. You will take damage if you step in it, so avoid it. When she casts Mistral Song, you can move to her sides or behind her to avoid damage.
Otherwise, repeat the above strategies until Garuda is defeated.
Completing the Quest
Defeating Garuda will complete one of the quest objectives for the Main Scenario Quest Lady of the Vortex.