In this map, the dragon veins will trigger traps that will hurt all units within range each turn. The thick woods terrain have no bonus effects but the “woods” panels provide bonuses. Thick woods can only be traversed by flying units so bringing in Hinoka and Subaki and pairing them up with other characters will help you cover more ground while having the option to switch if there's a risk of archers shooting them down. There's also a chest (Rescue) in the northeast corner of the map, near Kotaro's location. There's also a shrine maiden beside the chest that has a Sun Festal. She also has a non-lootable Wane Festal that can heal any of her allies up to 10 spaces.
Once the battle started, your foot soldiers will have no choice but to move around the thick woods. As you step on the ground to the south, the spikes will be triggered and units in that terrain will suffer damage at the end of the enemy's turn.
On the second turn, Takumi will arrive from the west side. You must bring Azura there to sing to him to bring him back to his senses. Once done, Takumi will be part of your group and you can order him as a normal unit. The dragon vein traps will just damage all enemy units within range so don't be afraid walking your forces there. Continue heading eastward and decimate the enemy forces until you reach Kotaro. Don't risk sending in small units; surrounding him before finishing him off is a good way to share EXP. After the battle, you'll also get Kagero as another new unit for your army.