In this mission, your objective is to seize the throne where Takumi is sitting. There's a ballista he can operate right in front of him as well. His retainers, Hinata and Oboro will be guarding the bridge and the stairs leading to the throne room respectively. Across the chasm, lies the entrances leading to the wall. It's recommended to bring your fliers here and pair them with your most powerful units in order to break through the defenses, and also take control of the ballista stationed there.
Furthermore, there is a couple of chests in the NE corner of the wall that you can loot. (Contains Boots and 10000g) Crossing the chasm with fliers is the best way to avoid walking around it and getting in range of the enemy ballista. Unfortunately, you only have a handful of fliers so you can only bring a handful of units at a time.
You can divide your forces. Your bulkier units (riders) should take the longer route and eliminate the enemies there. If you have limited flier units, you can have at least a healer stand by near your starting position so you can do a hit-and-run attack on the enemies across the chasm. Attack, fall back, heal, and repeat. Make sure you don't place them within the nearby ballista's range. Once the initial wave of enemies are dispatched there, you can attempt to separate the supports of your fliers and have them deliver more units by partnering up with them. This way, you can deliver your key units across. If your Azura is still a songstress, her sing can make this process a lot faster.
For your ground units heading west, make sure to take the path south of the lake to avoid getting in range of the ballista across the chasm. During the second turn, a lot more reinforcements will appear from the forts. Don't underestimate them; pair up your frontline units and keep your healers and spellcasters at the back. Fight them in the bottleneck south of the lake to avoid getting surrounded. If you're having problems holding that position, you can hold the forts near your starting positions and let the enemies come to you. Take note that western enemies (except the reinforcements) won't move unless you aggro them so might as well keep your ground units still while you're crossing the chasm; better yet, after you manage to transport them all.
Once you have enough forces on the other side of the chasm, you can start taking over the wall. Make sure to save your game before making any moves. After successfully taking over the wall, it's just a matter of moving all your units to Takumi's position and finishing him off. However, if you want to farm EXP, improve weapon proficiency, and relationships, you can use finish off Takumi and not seize the throne until you take out all enemies instead.
Once you take down the first ballista on the wall, you can use that to weaken the guards of the other ballista overlooking the chasm and finish the guards off with your units. Taking over the wall will give you these advantages so you can decide how the battle will go from here.