Dishonored: Dunwall City Trials: Burglar Walkthrough
Burglar is a stealth-based challenge. The goal here is to sneak into a mansion and steal six different eggs. Along the way, you'll have to collect as many valuables as possible to increase your score. Sneaking through the entire mission unseen will also increase your score.
There are many hidden nooks and crannies in the mansion which will reveal secret passageways and treasures, so you should try to interact with as many things in the environment as possible. Triggering certain switches on the environment will open up new paths.
You'll begin the challenge on a platform leading to the front gate of the mansion. Sneak through the gate and choose to head through either the front or the back door. Being spotted three times over the course of the mission will end it, so try to steer clear of enemies and take it slow. Use the HUD to find all of the valuables in the area, but don't make a beeline straight for them. You'll want to pick up anything even remotely valuable before finishing out the mission.
Use dark vision to see through the walls. This will make it easy to avoid the enemies and predict their patrols. Hoard all of the valuables from the walls and, when there's not much left to grab, head for the eggs, starting with the closest and ending with the one farthest from you. As you move around, try not to kill or knock out enemies, as this will impact your score in the end. Dark Vision will also help you to find the eggs, which is a nice bonus when navigating the mansion's various rooms.
Once you have all of the eggs, you'll have to leave the mansion without being detected too. Use Dark Vision to detect enemy patrols and you should be fine.