How To 

How To Complete The Kiddie Kingdom In Fallout 4

This is probably one of the easier areas to take over for one of the raider factions, so it's a good place to start with this DLC. The area is inhabited by a lot of ghouls, as well as toxic sprayers, so it's a good idea to come in full power armor for the radiation protection, or at least with a good stock of radaway and rad-x.

Step 1)Complete the quest 'A Magical Kingdom'.
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You'll have to search the tunnels, the funhouse, and the theater during this quest chain, the tunnels are an easy start as you won't encounter too much of a problem there, and there isn't much interesting happening in them to go exploring around them. Find the scene of Oswald and a ghoul and move on to the theater. This is in the King Kola castle area, and when you come in here you'll run into a bit of a brawl with a few ghouls, including Oswald the Magnificent. It's not too hard of a fight, you'll just have to deal with him performing a disappearing act and healing himself from time to time. You won't kill him here though, he'll be back later. Now you'll have to go search the fun house, which is probably one of the most annoying places in the whole park. Save option, and use your Pipboy light to navigate better, and you'll eventually make it through this area if you stick to it. Watch for the holes in the ground you can fall through in the last mirror maze.

Step 2)Finding Rachel.(Optional)
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You don't necessarily need to do this, but it will help you when you confront Oswald for the last time in King Kola castle, and is fairly easy to accomplish. Rachel is Oswald's girlfriend, and went out in search of a cure for why everyone was turning feral. You can find her in Bradenburg, which is in the far northeast side of Nuka World, just to the east of the map marker. Once you find and talk to her, you're ready to go talk to Oswald.

Step 3)Talk to Oswald and claim this territory.
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If you found Rachel, this is as easy as talking to him, and then claiming the flag to give the area to the gang of your choice. The flag pole is located just out on the balcony. You can also access Oswald's terminal and turn off the poison sprayers in the area, making it a bit safer to walk through again. If you didn't find Rachel though, you are in for a fight. Oswald is going to be tougher this time than last, as he will summon up waves of ghouls to bother you, sometimes legendary ones, and he'll heal up to full five times before you can finally bring him down. Killing him will get you his tuxedo, his hat, and his sword, while finding Rachel, or persuading him through hard speech checks, will net you only his hat and sword.

Now that you've claimed the flag pole, it's just a matter of deciding which faction deserves the area and assigning them to it.