You plan to rescue Minfilia from the Eulmoran Army, but the Exarch has asked you to entrust the task to the people of the Crystarium.
Requirements
This quest is available if you have completed the quest An Unwelcome Guest.
Starting the Quest
Talk to the Crystal Exarch to begin the quest. There will be a cutscene.
Speak with Lyna
Talk to Lyna to proceed.
Speak with Katliss
Go north and use the Aethernet Shard to go to the Crystalline Mean, then go southeast to the quest icon on the map. Talk to Katliss and there will be a cutscene.
Speak with Chessamile
Go northwest and use the Aethernet Shard to go to the Dossal Gate. Then go west to where the orange arrow is pointing on the minimap. You can go through either of the archways to enter Spagyrics. Talk to Chessamile.
Drink the Vial of Prince's Kiss
Without targeting anything, while standing near Chessamile, use the Prince's Kiss from the Key Items section of your inventory, or use the icon to the right of the quest name in your list of active quests.
Speak with Szem Djenmai
Go southeast through an archway to exit Spagyrics. Go east to the Aethernet Shard and use it to go to the Temenos Rookery. Go to the quest icon on the map and talk to Szem Djenmai to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Szem Djenmai to accept the next quest: Logistics of War.