Despite learning that your would-be ally is likely to refuse, you proceed to the Churning Mists.
This quest is available if you have completed the quest An Ally for Ishgard.
Starting the Quest
Talk to Alphinaud in the Dravanian Forelands to begin the quest.
Speak with Aymeric
You can either go northwest into the caves and talk to the Solemn Dragon at the end of the cave to go to the Churning Mists, or you can teleport to Moghome. Go to the quest icon on the map and talk to Aymeric. There will be a cutscene. (The moogle's name is .)
Blow the Horn
Go west to where the orange arrow is pointing in the minimap. Check on the sparkling Destination. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.
Speak with Aymeric Again
Talk to Aymeric to proceed.
Speak with the Imperious Wyvern
Go south to the quest icon on the map. Talk to the Imperious Wyvern to proceed.
Use the Duty Finder or Duty Support to enter Sohr Khai. Please see the Sohr Khai Guide for a walkthrough.
After you complete the duty in Sohr Khai and exit the area, there will be a cutscene.
Speak with Alphinaud
Talk to Alphinaud to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Aymeric to accept the next quest: An End to the Song. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.