Return to Vector, speak with soldiers before the timed banquet, and answer the emperor.
Walkthrough
At Vector, the emperor asks the group to speak with soldiers before dinner. Visit as many as possible during the timer; some conversations may lead to fights. When the banquet begins, remember the subject of your toast and listen carefully to the questions.
Banquet rewards depend on both conversations and answers. A separate save lets you retry if a particular reward matters to you. Afterward, travel to Albrook and board the ship with the designated party.
In Thamasa, stay at the inn, meet 
Strago and investigate when the house catches fire. Work through the burning interior and defeat 
FlameEater to rescue 
Relm. Heal and replenish supplies before heading west to the mountain.
Checkpoint
The banquet has two components: the timed soldier conversations and the subsequent answers. Keep track of the toast, and make a save beforehand if a particular reward matters. At Thamasa, carry enough recovery to get through the burning house and its boss before heading to the mountain.