After smoothing things over in the Wind Tribe Village, you go to Izumo to search for Ryoma and Takumi.
Before the Battle
You might want to include Hayato in this battle, because he starts at level 1.
Rout the Enemy
To start with, you will want to move your units out of the enclosed room, getting them out of the attack range of the enemy Mages.
Then have Corrin go southwest, because allies will arrive after turn 2. Have Corrin talk to the two allies, Hinata and Oboro, to get them to join you.
There are four Dragon Veins in the map. If you activate one, it will heal all of your allies.
Be aware that enemy reinforcements will appear from the stairs after a while.
There are some chests in the northwest and northeast corners, and they are behind locked doors. You can send a Ninja to open those locked doors and chests. Or you can defeat the paired Knight and Outlaw near the top of the map to acquire a Door Key and Chest Key. If you want both treasures, you will need at least one Ninja in your party.
When you are ready, make your way into Zola's room in the upper-middle part of the map and kill him and his guards to finish the battle. You might want to have your units rush into the room as soon as you have defeated the paired Knight and Outlaw to prevent the two Dark Mages in the corners of the room from blocking your path.
After the Battle
Afterward, you can move on to Chapter 10: Ninja Village.