With the stronger Ifrit now defeated by your hand, you are ready to take on the next re-summoned primal, Garuda.
This quest is available if you have completed the quest Ifrit Bleeds, We Can Kill It.
Starting the Quest
Talk to Papalymo in the Waking Sands in Vesper Bay in Western Thanalan to begin the quest.
Speak with Vorsaile Heuloix
Go to Gridania and go west from the aetheryte plaza to reach the Adders' Nest. Talk to Vorsaile Heuloix there to proceed.
Attune to the Aetheryte
Go to Coerthas Central Highlands and go to where the orange arrow is pointing on the minimap. Check on the Natalan Aetheryte. This will unlock the duty The Howling Eye (Hard).
Next Side Quest
After you complete the quest, talk to Papalymo in the Waking Sands in Vesper Bay to accept the next side quest: In a Titan Spot.