Once you enter, you are greeted by Motonari, who seems rather peaceful. After that cutscene, you will then enter the battlefield. You will also be introduced to the second mode of battling, Capture the Flag, literally. Similar to other games which features this mode, you have to collect all the flags to win, it's also the same for the enemies plus with defeating all your pokemon to win. So make sure to keep your pokemon very healthy in this fight.
Let's analyze the enemy's pokemon First up is Motonari's Snivy. Let all starters, it has a ability which increases attack when it's almost down, again, not much to worry as it won't really hurt your pokemon that much. And then we have Motoharu's Pansage, in which is rather weak, although it's melee ability (if he has one) can be a little bit worth noticing. If a enemy hits your pokemon and Pansage is in front of the pokemon, it can hit your pokemon for more damage. So be a little wary of that Pansage, they both have Vine Whip, which can attack three square in a row in front of them. SO keeping your pokemon separated will help decrease the damage.
And then we have Takakage and Takamotoe's Sewaddle. These guys can be rather annoying. Sorta consider them the Zubats of this game. Why? It's attack Bug Bite. If it attacks you and you're holding on to an item, say goodbye to it. Plus they'll use it once they get an item that can heal them, like potions and that stuff. And on this stage, they are really annoying thanks to grass cloak. At least one of them has it. With it, they take less damage thanks to using the grass as a defense. Since you have a fire pokemon i'm assuming, you can use them to dispose of those grass cloaking Sewaddles. Otherwise you'll be there for about 5 turns killing a Sewaddle.
Now for the stage. There are two things you need to notice about the stage. As you can see, there are small bushes around the stages, these are hidden passages. If you go in one, you'll be taken to a different part of the stage, maybe somewhere close, or far. Motonari's Snivy will take one of these hidden passages to get to one of the flags in this stage. The last one is every turn, a vine bridge will form, allowing the defender's pokemon to cross and head for one of the bridges, only one of the Sewaddles will take this route to get to the flag. Make sure you have a strong pokemon before you go towards that flag.
Once you collect all the flags, you win and Motonari will flee from his nation since you beat him.
Once you take down Greenleaf, you can now go and recruit members with grass pokemon now, you should be able to recruit some trainers after the battle if you have killed them in four turns or killed them with a fire pokemon.
If Greenleaf was your first nation you have taken over, head over to Fontaine and conquer that nation with your awesome grass pokemon, or if Greenleaf was the last nation you took over, head over to Fountaine page and scroll down to Fontaine: Aftermath.