It's a Defend-This-Area-For-11-Turns mission, and you have chokepoints (at first just two, but it opens up to four fairly soonish, and you have to watch out for the Sky Knights since they can go over the water, letting them manuever around the land-based chokepoints) and ballistae (two, plus a magic-ballista-thingy, so bring Odin/Nyx and Niles, and also Mozu if you made her an Archer (which you should, in my opinion, because she struggles with taking hits, so it's better to keep her in a class that doesn't get attacked as often) to man those). It's fairly simple unless you want to get all the villages (which you should, though it's optional so don't feel like you need to, just grab the two villages at the top and decide on the lower two as you go), in which case it can get a bit tricky.
Takumi's the boss on this map, and he's sitting on a Dragon Vein (they let certain characters alter the map. Takumi is one of these characters. This will be important later), but he won't move so you don't need to worry about him moving up to punch some holes in your defensive formation. Also, Hinata and Oboro are waiting on the sides (annoyingly, Oboro's able to attack whoever you send to the lower right-side village, so make sure your village-visitor can survive her), and they're probably a fair bit stronger than everyone not named Takumi on this map, but they won't move unless you go into their range (and I never went into their ranges except to have Camilla visit the lower-right village, and I Rescue-Staff'd her out before ending my turn, so I dunno if they'll actually move or not, but they probably will). Also, prepare for many reinforcements, some of whom can fly (so they can, as mentioned previously, go over the water and around the chokepoints; eliminate these as soon as they're in range, because between their ability to ignore chokepoints and large movement range they'll reach the area you're defending quickly if not addressed as soon as possible).
For party composition, I recommend that you bring Corrin (because you must, and he/she's probably a solid fighter so he'll come in handy wherever you put him; the left side is a good spot for him, though Corrin can work anywhere since he's fairly versatile), Felicia and Elise (healers are very valuable, and knife attack stat drops can come in handy if nobody around Felicia needs healing), Odin/Nyx (for the magic-ballista-thingy, since it's quite useful for controlling the left and a small portion of the lower area of the map), Niles and Archer!Mozu (for ballistae support, and also to slaughter those annoying Sky Knights; a Heart Seal'll cost you a bit, but it's worth it to have two bow-users) and Effie (defensive wall on a defensive map, need I say more?). Other good choices include Arthur (lots of lances on this map, so he'll get mileage out of his weapon triangle advantage, but he might get critted due to his crap luck), Silas (he's good for putting on the left side to block it, since he uses Swords, which frees Corrin up to help elsewhere, though Silas's ability to use Lances and increased movement range over Corrin can make him a bit more useful elsewhere than Corrin; he's not wholly needed, but you probably won't regret bringing him along) Azura (guard her very carefully, especially if your Azura is as squishy as mine is (seriously, I think she still has 16 HP at the end of Chapter 12), but her extra-turn-granting is quite useful, and she can finish off enemies in a pinch (only as a last resort)), and Villager!Mozu (she's not as helpful as Archer!Mozu, but you can bring her along to train her up if you have an extra slot on your team). Beyond them, bring who you're comfortable with (though if your Odin and Nyx are both fragile, bring the less squishy one; don't bring both unless they're both kinda durable, since they'll probably get attacked at some point).
From the start, have someone with a sword (I used Mercenary!Silas thanks to a Heart Seal, you could use Cavalier!Silas or Corrin) rush off to the upper-left village (contains 10000 Gold. You want this) on their way to the left-most wall, which will be broken by enemies after a few turns, so you want to get over there and stop them at the wall. Also send Elise that way, to patch them up when they get hurt. Additionally, a couple of Oni Savages start on the other side of that leftmost wall I mentioned, so have Odin/Nyx pelt them with the magic-ballista. On the right side, have Niles/Archer!Mozu go to the upper-right village (contains a Master Seal. You want this) on their way to the right-hand ballista, and have Effie go with them, since the bottom has axe- and lance-users that Effie won't be too useful agaist, while the right side has Archers who can barely scratch her so she can block them off from attacking Niles/Mozu), and have the, defend that side. In the center, park Corrin or Arthur on the right-side chokepoint, and have Felicia heal your blocker as needed. Whoever out of Niles and Mozu isn't manning the right side needs to run down and man the central ballista. Additionally, if you only have one bow-user, use them for the center ballista, it's far more important than the right-side one (and if this is the case, send someone out along the right side to back Effie up; not Azura or Villager!Mozu, she'll get killed in one or two arrows to the face). Eventually, a hole will be opened up on the center-left wall, so smash those intruders (mostly lance-users, but also ninjas, so be mindful of any stat drops they cause) with the rest of your party (be careful not to enter Hinata's range during this, since he won't move if he can't attack you). After defending the center-left wall, visit the lower-left village (don't remember what's in it, but hey, free stuff).
After a few turns, you'll get three new party members around your starting point. These are Beruka on the left, Selena on the right, and Camilla in the center, and I'm going to go into them briefly now.
Beruka is a Wyvern Rider. She can fly and wields Axes. Because she's a flier, she's especially vulnerable to bows, so don't send her to the right. Instead, have her aid in smashing the center-left attackers, or the leftmost-side attackers if Corrin/Silas is having trouble there. She'll be useful to you here, just keep her away from bows (not hard, just don't send her to the right).
Selena is a Mercenary. She wields Swords and has balanced stats. Have her back Effie up on the right side, though she can pitch in elsewhere if Effie doesn't need assistance. Generally a good unit for this chapter.
Camilla is a Malig Knight. She can fly and wields Axes and Magic. She can crush most enemies on this map, and is quite a bit stronger than Beruka, but she doesn't get as much experience out of fights as your other units, so use her sparingly. For this chapter, think of Camilla as a Bag of Dragonite: use her sparingly, and only when absolutely necessary (ie. if you'll fail the mission unless this one enemy dies/is blocked from reaching the need-to-defend tiles), so that your other units can get up to her level. A good use for her is to visit the lower-right village (don't recall its contents either, sorry), since she can probably survive an attack from Oboro (though maybe wait for the final turn to do this, to avoid Oboro suddenly chasing your not-Camilla units).
So, now you've received reinforcements, and you're defending. It's been 7 turns, and it's not that tough unless you get on an unlucky streak, so you're probably wondering to yourself,
"Kirbys, this is easy! Didn't you say this was where Conquest gets hard?"
And Takumi answers,
"SAY GOODBYE TO YOUR CHOKEPOINTS, TRAITOR!"
And removes the water from the map with that Dragon Vein he'd been standing on.
Which doesn't look so bad, at first. After all, it looks like it's just a minor visual difference on the map. It's not like the enemies can just walk on the new dry areas to bypass your chokepoints-
Oh, right. They can. And they do.
And when they do, they'll make a beeline for your previously-safe squishies.
And the exit you're defending.
And with a single move, Takumi turns what was previously a simple defend-the-area chapter into a mad scramble to protect not only the uppermost area of the map (that's where the exit you can't allow enemies to reach are. They're the green tiles), but also to ensure the safety of your less durable units who were previously safely settled behind your stronger units but are now vulnerable.
Welcome to Conquest. It's not gonna be easy.
I feel like I should note that the next chapter is easier, mostly because it's a fairly simple defeat-the-boss map and all of the tough enemies outside of Hinoka can be ignored (unless you're after all of the treasure, then the staff-dude'll annoy you with his HP-halving; don't send any important fighters up the right-hand side until you've exhausted that staff's 3 uses), but Chapter 12 ramps it back up.