Spoiling the party means making the guests upset, so you can kill guards, the maids or anyone else as long as you aren't caught and an alarm isn't rung. I'd recommend starting the level using an invitation either found on the way into the front yard or found in the Art Dealers safe from the Golden Cat mission. Alternate routes are to use the building on the far left near the mansion where the guard and Tall Boy are patrolling. Go up the stairs past the weepers, and out the window on the right to an open window above it. That is the guards barracks which has a key on the wall to unlock the door to the mansion grounds. If you can't or don't want to use those options you can use Blink to get onto the mansion walls between the fence by going from the rooftops to the streetlights to the fence post. However you gain access to the mansion is fine as the guards assume you are rightfully there even if you just jump from the fence in front of them.
Once you get in the mansion you have three options. You can play the game the Boyles want and gradually figure out who the right sister is, with or without help from Ms. White in the Moth mask. You could sneak upstairs by waiting for the guard to leave for the basement and go from room to room to find out which Boyle is which by reading their diaries. Finally, you could just murder all three in secret, usually by using slow time and shadow kill to dispose of the bodies.
The non-lethal option is to go find Lord Brimsby in one of the back rooms. He will explain that he is aware of your mission and in love with your target. He asks that you bring her to him so he can keep her safe. You then are told which one is the target, you then speak to the target, tell them their life is in danger and for them to go to the basement with you. When you get her to the basement, knock her out by choking or sleep dart, just open the door by the nearby switch and carry her down to the waiting boat. You can then either go back to the party or leave by the nearby sewer exit.
You will get the trophy when the level ends after you meet with Samuel as long as when you leave the party is still going.