Taking Independence

Taking Independence is a quest and achievement/trophy in Fallout 4.

Quick walkthrough
You must assist three settlements before Preston Garvey will approach you with this quest. He asks you to meet him at The Castle (Fort Independence) which was previously taken from the Minutemen. Upon meeting Preston and three Minutemen at an old run down store near Fort Independence, you go through some dialogue with Preston and the others before being prompted to choose a plan of attack (there are three options). After choosing one of the plans of attack, the others get into position before you engage the Mirelurks inside the courtyard of Fort Independence.

After clearing Fort Independence of the mirelurks, Preston asks that you clear the area of any egg nests. While you are clearing the eggs, the mirelurk queen spawns and you must defeat her. Once that is done, you are to clear the area of any remaining eggs, then meet the Minutemen in the middle of the courtyard where the radio transmitter is located. After searching the workshop within the Fort, you are to provide 10 power to the radio transmitter. Afterwards, talk to Preston Garvey and the quest is completed.

Detailed walkthrough
Once you have established approximately five settlements (counting Sanctuary) for the Minutemen, talk to Preston Garvey. He'll tell you about the Castle, the former headquarters of the Minutemen, and discuss his desire to retake the building to show that the Minutemen are back. Offer to help, and he'll tell you to meet him outside the Castle.

It is strongly recommended that you bring power armor and at least one heavy weapon. It may also be worthwhile to bring the parts for a nuclear generator, or two of the medium gas generators, and a little bit of wire.

The hike to the Castle will take you through South Boston and past a number of both Raiders and Super Mutants in equal measure. Garvey is waiting for you in a destroyed Sullivan's west of the Castle with three other Minutemen. DO NOT APPROACH THE CASTLE BEFORE MEETING THEM. It is crawling with mirelurks and has nasty surprises in wait. Additionally, the Sullivan's has a bunch of equipment on the counter that may be useful--including land mines.

Talk to Garvey, and he'll discuss your options. The three Minutemen will offer various potential plans of attack--a direct assault into the courtyard via the breached northwest wall, a pincer through the breach and the main gate to the south, or setting up a firing line outside the northwest breach and drawing the lurks out to your guns. Pick whichever suits your preference, and then wait for the Minutemen to move into position. When all's in order, launch the attack.

There are about ten mirelurks of varying strength inside the Castle. Aim for their soft undersides, as chipping away at their shells is a sure way to just irritate them and get yourself clawed. Once they're all dead, Garvey and the Minutemen will observe the egg clutches laying around--if they're not cleared out the mirelurks will keep coming back.

Approaching the egg clutches will cause several of them to hatch mirelurk hatchlings at you--effectively radroaches. Either handle them as they come or take out the clutches from a distance with explosives--this will deny you those tasty Mirelurk Eggs, however, which make a fantastic omelette among other things.

It is strongly recommended that before you begin clearing them out in earnest, you lay some mines on the breach in the southwest wall--not the one you came in on, the other almost-destroyed one. If you don't have a heavy weapon, head to the easternmost room in the fort--there's a missile launcher and some ammo on a table in there. There's also a flamer kicking around, but Preston is likely to requisition that.

The reason for all this will quickly become obvious. After you've destroyed a few clutches, the entire Castle will shake, and a Mirelurk Queen will emerge from the lagoon--the "sea monster" that destroyed the Castle in the past. She'll make her way through the southwest breach and into the Castle courtyard, at which point she'll start killing anything she can reach--Preston and one of the Minutemen are essential, but two of them aren't, and you certainly aren't. Try to keep a moderate distance--too close and she'll tear you to shreds, but too far and she'll spit acid at you with serious effectiveness. She is NOT to be underestimated, but keep up the fire and keep her attention away from your squishy allies, and she'll go down.

Once the Queen is dead, clear out the remainder of the egg clutches--don't forget to check on top of as well as inside the walls! After they're all gone Preston will tell you about Radio Freedom, and task you with getting it up and running. This requires ten power all on its lonesome--either one large or two medium generators will do the trick. Once Radio Freedom is powered, talk to Preston again to complete the quest.

Behind the scenes
The presence of mirelurks at the Castle may be an allusion to the Lobsterback infantry that the Minutemen fought during the Revolutionary war. This could also be believed as there is a "queen" present, symbolizing the monarch. The queen is in the castle, which you must take.

Bugs
DO NOT CLEAR THE CASTLE BEFORE THE QUEST. If you do, then Preston Garvey will just tell you to focus on taking back the castle and can't continue. No solution is known at this point. *SOLUTION* Clear any nests of eggs, the queen will still spawn and the quest will go on.
 * Companion Preston Garvey will follow you around the whole game if you start, but don't finish the quest. However you will be unable to speak or interact with him. This essentially gives you 2 companions.solution??
 * When the quest is concluded Preston will no longer be available as a companion, and will only give one-line NPC responses when conversation is started. This can render the Minuteman storyline impossible to finish as he remains at Sanctuary and no longer gives out quests. On PC the solution is to target Preston in the console and type "removefac 00075D56" (without quotes) which should allow him to be recruited as normal.
 * After defeating the Queen and clearing out the Fort, Preston Garvey will sit on the wall doing nothing with no speech options. This may be solved by sitting on the chair and waiting.
 * After killing the Queen, the remaining Minutemen become enemies and attack.
 * After killing all the Mirelurk and Eggs the Queen never spawned, used console command "killall" and noticed she died very far under the game, found her using "tlc" and was able to loot her. I recomend saving the game before attempting to do this quest, I had no other savedgames than the quicksave one.