You have traced the rumor to a teahouse and are directed to inquire at the docks.
Requirements
This quest is available if you have completed the quest The Sword in the Stone.
Starting the Quest
Talk to Yugiri in Kugane to begin the quest.
Speak with Soroban
Go west to where the orange arrow is pointing in the minimap. Talk to Soroban and there will be a cutscene.
Speak with Alphinaud
There will be a glow around Alphinaud, indicating an instanced battle. Check on him and there will be a cutscene, and then the battle will ensue.
Solo Duty: Hope on the Waves
First, defeat any Signifers on the battlefield, then try to pull all enemies near Yugiri so they will be within the blue circle attack marker near her. Dodge the line attacks from the Magitek Rearguard.
Afterward, follow the others upstairs, and there will be a cutscene.
Phase 2
Defeat Signifers first, then focus all attacks on the Magitek Rearguard. Try to pull all enemies into the dust circle so they will take damage from it.
Afterward, attack the Magitek Hexadrone while keeping your distance from your allies so they will not be hit by the circle attack 2 Tonze Magitek Missile. Move away from the Hexadrone whenever it casts Circle of Death, a circle attack centered on the Hexadrone.
When you are marked with an attack marker that follows you, move far away from your allies while staying out of the circle attack markers around the glowing Magitek Bits. Then when the proximity attack marker appears, run far away from it while continuing to attack the Hexadrone.
Afterward, pull all enemies into the large blue circle marker, and use multi-target attacks on the enemies.
Afterward, there will be a cutscene.
Speak with Alphinaud
Talk to Alphinaud to proceed.
Join Alisaie
Go southeast to where the orange arrow is pointing in the minimap. Talk to Alisaie and there will be a cutscene.
Speak with Soroban
Talk to Soroban to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Yugiri to accept the next quest: Elation and Trepidation.