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. She is tough and a good way to kill her is to quickly lay a number of mines directly to the shore before she appears, as she will crawl out of the water, right into the mines. This will weaken her enough to be able to be killed before she could cross the wall to wreak havoc. Once you have defeated her, 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
The eggs can all be destroyed at range without triggering them hatching. If you use this approach you will miss out on lots of Mirelurk Eggs and Meat however.

The radio transmitter requires 10 power to run. You will most probably have to bring enough junk with you to be able to build a large power generator right away.

Trivia
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 Preston Garvey will just tell you to focus on taking back the castle and cant continue don't know of a solution
 * 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.
 * 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.