After a clash with prisoners in Nohr, you must prove yourself at the Hoshidan border.
Seize the Building
Starting with this battle, you can use the Pair Up command. A unit who pairs up with another unit will be placed in the back. For example, if you move Corrin next to Gunter and have CORRIN choose the Pair Up command, GUNTER will be in front.
Hans will move on his own, and if you don't intervene, he will rush onto the east bridge and attack the samurai, taking valuable experience away from your units. To prevent this, at the start of the battle, have Jakob/Felicia pair up with Gunter, then have Gunter ride as far east as he can go, onto the bridge. Before ending their turn, switch them so Jakob/Felicia is in front, and have Jakob/Felicia attack the samurai that is in his/her attack range. Meanwhile, move Corrin as far south as he/she can go, toward the southern bridge.
After the enemy phase, Jakob/Felicia will have killed the first samurai, and the second one will now be injured and in Jakob/Felicia's attack range. Have Jakob/Felicia attack this final samurai to kill him, then move Corrin farther south, as far as he/she can go.
Next, you can get a little more experience for Jakob/Felicia by moving them east so that they can attack the samurai on the fort. Be sure to put them one square away from the fort, rather than directly next to it. Otherwise the archers beside the fort will kill them. In Lunatic mode, the samurai on the fort starts out in front, so Jakob/Felicia can safely attack it without taking any damage. During this player phase, have Corrin stand on the southernmost Dragon Vein but DON'T activate it yet.
After the next enemy phase, you can have Jakob/Felicia attack the fort samurai again, unless you are playing Lunatic mode, in which case the archer on the fort will be in front of the samurai, so Jakob/Felicia will be attacked if they stay there. In Normal mode, Jakob/Felicia can finish off the samurai on the fort. In all modes, don't try to go through the fort, because the archers will probably kill you. Jakob/Felicia and Gunter should all start moving south to where Corrin is. Hans will have died at this point. There is no way to stop him from running directly to the fort and getting himself killed, so just ignore him.
At this point, you will not be attacked unless you go into any enemy's range, so take this time to put Jakob/Felicia on the southwest fort, then keep ending your turns until Jakob/Felicia is fully healed up.
Separate Jakob/Felicia and Gunter. Put Gunter south of where Corrin is standing (Corrin should be on the southernmost Dragon Vein). Put Jakob/Felicia to the left of Corrin. Then have Corrin activate the Dragon Vein. With support from Jakob/Felicia and Gunter, Corrin should be able to survive the attacks of the enemies that will come across the bridge after you have activated the southernmost Dragon Vein. Be sure to keep your units in that position until the bridge enemies have come across.
After the bridge enemies have attacked, have Corrin, Gunter, and Jakob/Felicia finish them off.
Before you go east across the bridge, be aware that after you reach the southeast area of the map and end your turn there, some Sky Knights will come out of the southernmost fort, and they will move toward your units whether you are in their attack range or not. However, they aren't really that strong. Your team will be able to kill them as long as your three units stay in adjacent squares with each other so they can support each other's attacks.
In the southeastern area of the map, you have a choice of putting your units in a square outside of the boss unit (Omozu)'s attack range, or just going straight for the boss. If you do enter a square outside of the boss unit's attack range, be aware that the boss unit will support the archer's attack. I would instead recommend attacking the boss unit directly.
However, Corrin in particular has a rather low percent chance of actually landing a hit on the boss unit, so have him pair up with Gunter so that Gunter is in front, and have Gunter attack the boss unit. Then immediately have Jakob/Felicia attack the boss unit from the tile next to Gunter so that Gunter will support the attack. With any luck, you will kill the boss unit.
At that point, you can either seize the tile that the boss unit was standing on and end the battle right away, or you can kill the Sky Knights, then kill the archer (if there is one), and you can even go northeast to try to kill the archers around the fort there. In Lunatic mode, the paired archer/samurai will come toward you if you approach from the south, so be prepared for that.
Then when you are ready, you can seize the tile to end the battle.