After some surprising revelations in Hoshido, you must battle some shadowy enemies.
Rout the Enemy
The objective is to rout the enemy. Some of the enemies are using Wyrmslayers, which will cause a lot of damage to Corrin.
Corrin can kill all of the enemies on this map in one hit, except for the boss. However, if you let the Wyrmslayer enemies come to Corrin, they will kill Corrin in one hit, so be sure not to let this happen. In addition, since the Mages will attack Corrin from one tile away, you should avoid letting the Mages come to Corrin, because Corrin will not be able to strike back on that turn.
During the battle, Ryoma will fight the boss unit, but Ryoma will die within three to five turns. It probably isn't possible to kill the boss unit before it kills Ryoma, but Ryoma will still come back even if you are playing Classic mode.
There are two sword-wielding enemies on the left side of the fountain. They aren't using Wyrmslayers. You should move Corrin into the attack range of BOTH of those enemies. That way, both enemies will try to attack Corrin, but Corrin will take no damage and will kill them with the counterattack.
On the next turn, move Corrin clockwise toward the right, and use Azura to sing to Corrin so that he/she can go all the way to the the Wyrmslayer enemy on the right and kill him.
After that, in Hard and Lunatic mode, have Corrin kill the Mage on the right side.
At this point, heal up whoever needs healing, then move Corrin to the left side of the fountain and keep Azura near Corrin, then have Rinkah pair up with Kaze (putting Rinkah in the back) and have the two of them go just inside of the attack range to the RIGHT of the fountain. This will cause all of the enemies south of the fountain to start moving toward you. Putting Corrin to the left of the fountain before you attract those enemies is the key to winning this battle in Hard and Lunatic mode, because the paired Wyrmslayer enemies will move to the left toward Corrin, while the mages will move to the right toward Rinkah and Kaze.
If done correctly, you can have Corrin kill the first of the paired Wyrmslayers, then have Azura sing to Corrin so that Corrin can kill the final Wyrmslayer. This is really the only way to get rid of those two Wyrmslayers; your other units aren't strong enough to withstand the paired units' attacks, so you have to have Corrin kill both on the same turn.
Meanwhile, Kaze and Rinkah should retreat so that they are close to Sakura without allowing the enemy range to reach all the way to Sakura. If you position Kaze and Rinkah properly, they won't be killed by any of the approaching Mages, and with luck, they will kill one of those mages.
Once Corrin has gotten rid of the paired Wyrmslayers, have Corrin kill any Mages that are an immediate threat to your weaker units, having Azura sing so that Corrin can kill two enemies on that turn. Rinkah and Kaze should be able to finish off any Mages that have already taken damage, but be sure to have Sakura keep Rinkah and Kaze healed up.
Finally, send Corrin down to the boss unit, which will not move from its position. Put Sakura outside of the boss unit's range so she can heal Corrin if necessary. Only Corrin is strong enough to kill the boss unit, so don't send anyone else.