There are two ways to get yourself into the Boyle Estate. You can head in the back way, via a building filled with weepers, or you can use the invitation that you stole from the Artist's safe in the House of Pleasure mission. Either way works fine, but there's a Bone Charm in the weeper-infested building. As you go, check out the short metal bridge spanning the channel between the Pratchett Warehouse and the Boyle Estate. With the Boyle Estate in front of you, go to the left to find the Rune in the channel. Just follow the stairs down to the water. You can typically sneak around the weepers by the bottom of the stairs.

Along the way to the Estate, you'll find a Bone Charm. There's a short metal bridge going to the Boyle Estate. Cross it and approach the Estate. When you get across the street, turn to the right and follow the street to find a second apartment filled with weepers. The charm will be on the top floor.

If you simply decide to use the invitation, you can actually sneak out later using Blink and get back in, via the gardens where you'll also find Shaw. There will also be a blueprint for Spiked Grenades on the table by the guard who checks your invitation. You can reach the gardens via the door in the back of the main room of the party, but you'll want to explore the Estate a bit before committing to any mission critical objectives.

When you enter the party, it'll be under the guise of a guest. That means you'll have to act like a regular civilian, and performing any of the following actions might ruin your disguise: using powers in front of guests (other than Dark Vision,) firing a weapon, using a lethal gadget, harming an NPC, and trespassing. As you enter the party, you'll find a guard keeping the upstairs off limits. If you're opting for a clean and clever approach, the stuff up there will be practically essential, so you'll have to get upstairs at some point. Scope out the room to the left, which will be the main room of the party. A lengthy table will be covered in food and drink that you can consume to restore bits of your health, or that you can share with certain party guests to get privelaged information. The double doors directly to your right as you enter the room will lead out to the garden, where you will find Shaw. If you want to practice your dueling, head out there now.

When you deliver the letter to Shaw, he will become outraged and challenge you to a duel immediately. With his guards present to monitor the duel, Shaw will take up position and begin a countdown from three. Grab the pistol from his case and take up your position. You don't have a ton of options here; if you're looking to game the system and win the duel by default, you can slow dow time to take out Shaw with ease; his guards might not like that, though, and this may prompt them to attack. You can also switch out your pistol for a sleeping dart at the last second if you don't want to kill anyone.