After refusing to choose a side, you must distract Xander and Ryoma to escape.
Defeat Both Bosses in 5 Turns
There are two boss units, a Wyvern Rider and a Samurai. If you look at the map, you will notice that the Wyvern Riders are on the other side of the river and it would take a while for your units to go there. However, all of the enemy units will come toward you whether you are in their attack range or not, so you don't have to worry about running out of time to defeat the boss units.
Start by going across the eastern bridge to fight the Hoshidan enemies. By the time the Nohrian enemies reach you, you will probably have defeated most if not all of the Hoshidan units.
After the battle, Lilith takes you to your castle in the astral plane and walks you through creating buildings. At this point you can have Support conversations with your units, invite an ally to your private quarters (be sure to select someone with a heart icon next to the name because this will ensure that your relationship will improve), collect resources, and buy stuff from the shops.
Be sure to feed Lilith. You might want to check on the crystal ball to visit other castles (if you are connected to the Internet) because this will let you gather resources that are unavailable in your own castle, giving you a wider range foods to give stat boosts to Lilith.
When you are ready, press Start to go to the castle menu, then choose Next Battle. There will be several options. The Dragon's Gate lets you purchase DLC (be sure to check for free DLC). You can also change the difficulty here, and side battles will be listed here as well.