After the scene, you'll be facing off an Invader army with fliers. Setsuna and Takumi will be deadly against these enemies so you should use them. There are three dragon vein points in the ship; all of which will trigger a storm that can slow down enemy fliers to your advantage. Take note however that allied fliers will also become affected by the storms. The only way to get past them is by flying on the side of the ship.
At the start of the battle, activate the nearest dragon vein then move westward. Before the start of the second turn, Reina will appear. She's a Kinshi Knight, a flier unit that can wield the bow and naginata. She'll be an independent unit but she will approach your group. You have to talk to her using your avatar to recruit her to be part of your group.
Reina can easily decimate the enemies with her large movement area and her bow's bonus damage against enemy fliers. The enemy fliers are not to be trifled with easily. They have high accuracy and damaging attacks as well. Continue defeating all enemy fliers since there will be reinforcements that will arrive in the following turns. Keep healing your units and don't spread out too much individually and you'll conquer this map with ease.