Part II - The Palace
The approach to the palace is pretty light, and very talky. You'll keep running across enemies in pairs- let them finish their conversations, then take them out one by one.
Once you reach the far station (either by riding the rails or swimming across and climbing the rock), everybody's talking about the Duke's body double.
Terrible opsec, but handy for you- you may need this intel later. Get around the trio of guards at the entrance by sneaking along the waterway to the left- whether you want to choke out the guards themselves is up to you, but they are carrying coin.
You have easy access to the roof now, but it's probably best to go through the doors here and into reception and dining. The redguard here can be troublesome later, but now he conveniently keeps his back to the main entrance. Choke him out and hide him behind a tree in the vestibule.
There's a guard sitting on the steps to the left in the dining room you can take out as well- just don't get too overconfident. The witnesses here may be in a drunken stupor, but they'll react to running and or mayhem. Or being stepped on. From the vestibule, you may also want to Blink up and take out the guards on the balcony here. Only one is conscious, but his placement on the banister makes him an incredible pain to take out softly- even if you're practically perched on his shoulder.
Best bet is to drop down from the chandelier and punch in his face before he's twigged to what's happening. Choke the iniebrients into a more permanent slumber, but be aware of the clanker slowly patrolling the dining room balcony.
From here, paths diverge. This mission is little bit like a game of Clue- while the layout remains the same, each playthrough will be set up a little differently.
Your basic gameplan in this- locate the Duke and his double, either of whom may be in one of five locations. Discover which ones by scouting the Palace yourself, or by overhearing conversations and reading notes left by palace staff. A secondary sign is that locations with a Duke will have an extra complement of guards. Once you've located the ducal twins they'll show up in your mental radar, making them easy to find again (though the Palace is really not that big, and they never change rooms).
The next step is to determine which one is which. The surest way to lurk nearby until the Duke figure declares that he needs some solitude, and shoos the guards from the room. The Duke himself will mutter about his past and his family, while the Double will pull out a cigar and mutter about the hassles of being a double.
If possible, approach the double first. You can walk right up to him without triggering a detection. Tell him you know his identity, and he'll give you a plan for pulling a switch- but it involves knocking out the real Duke and stealing a medallion from his body. Kid's stuff. A new marker will now show up- the place in Duke Abele's Chambers where you need to put his unconscious body. Make sure you have a clear path between the Duke's current location and that new marker. If he's already in his chambers, you're golden, otherwise you may want to clear away some guards and/or civilians. You'll definitely want to secure the chambers themselves, and unlatch the inside doors for easy entry later. Another quick avenue of approach is a rooftop access that connects to the elevator shaft.
As with the double, you can walk right up to the Duke to discuss his fate- just be sure to punch him out immediately as the conversation ends, or he'll go for help.
Afterward, drag him to his chambers to trigger a cutscene, and an orderly transfer of power. Obviously, there can be no one way to tackle this level, as the objectives change position with each playthrough, but there is a detailed breakdown of locations below- use that in conjunction with the map to plot your course. In general, this level is very easy to traverse- most rooms have at least three points of access, and the sloping roofs connect every room with either terrace or balcony access, which is almost all of them. You can also use the seaside rocks to skirt your way around the building exterior, and the elevator shaft and several secret passages to worm you way through the interior. If you find yourself often getting lost or turned around, just try to keep track of where you are in relation to the big dining hall. It's the hub around which the palace turns, and and most places are just a roomswidth or two away from it. That said, let's start with the location highlights, beginning with the second floor (really the main floor of the complex).
Two gentlemen in conversation here- when they're done, one will head out to the patio. The nearby dressing room makes an ideal body stash, and a few coins can be gleaned from the pool grate.
Grand Throne Chamber-
Watch out for the bug zapper, which has a wicked range and no qualms about electrocuting you in the middle of a conversation with the Duke or his double.
Blink to the near chandelier, then atop the curtains, then hug the wall until you can pull out its oil.
Bone charm on the throne (Bonecharm 4/7)
First Captain's Office-
Blink behind the captain, loot, concuss. This room hold the remains of game of mumbledypeg gone horribly wrong, as well as a safe. The safe combination is in the Duke's Office- once opened there are some ingots and a Rune (Rune 4/5).
Small windows offer outside access here. There's a nearby barracks room outside this one, but it's tiny, the sleeping guards are lootless, and there are only a few coins to be gleaned.
Tiny windows offer outside access from the area by the vault dome. The people within are all prone, but very skittish (they also freak out about dead bodies, even though there's already a dead body in the room). The strategy here is to get seen, wait for the two live ones to jump to their feet, sleepdart the one in the rear, and punch the near one in the face before she becomes fully alarmed. No detection, no bodies seen. You could use the nearby bottle of chloroform here, but you're better off saving it for the poker game upstairs. Instead, grab the sleep dart jutting out of the table here to make up the loss.
You'll also also want to grab the bonecharm by the dead body (the one that nobody freaks out about at all)(Bonecharm 5/7).
If there's no Duke here, then it's inhabited by two blueshirts and a maid (with the clanker patrolling the Vault occasionally casting a glassy eye this way). Best approach is via the trellis or the lower stairs, but opposition is minimal- as is the loot. The guard is drinking something flammable, though, if you're on your way to the bloodfly hives below.
Target Range- Not an official location, but a handy landmark (again, nobody freaks out about these dead bodies). The far point of this promontory, behind the target wall, is a good place to stash bodies.
Third Floor Locations-
The main player on this floor is the clanker patrolling the Dining Hall Balcony. It's hard to take out without rousing somebody downstairs, and it wanders through audio range of a large number of locations. Luckily it's pretty slow, so you can schedule your silent takedowns around its patrol route.
The Poker Game- Accessed via the stairs up from the opium den, the dining hall balcony, or the terrace windows. The first route is ideal, because it allows you to snag the chloroform bottle from the den.
Blink up to the light fixture, shoot a sleep dart into the guard passed out behind the bar, and lob the chloroform right in the pot. Boom. Not a lot of loot to show for it, but satisfying nonetheless, and it opens a route that allows you to avoid the central clanker. There's also a Vault entrance outside, but we don't need to get there yet, and there will be easier ways once we do.
Fourth Floor locations-
Duke Abele's Office-
If unoccupied by one Duke or the other, it is guarded by a single blueshirt and a wandering maid. Get atop the bookcases here for ease of mobility and asphyxiation. Blueprints for blade conversion in cabinet near the hall window (Blueprint 2/3).
Audiograph on the main desk, and the First Captain's safe code on a lesser desk, by the typewriter.
Painting on the wall above the fireplace (Painting 2/3).
Scrimshaw behind glass, but it will wake the clanker here. It can be rewired & self destructed without alerted the other clankers, though.
Delilah Copperspoon's Chambers-
If entering from the hallway, wait for the blue shirt in the first room to take up position near the door, then choke him out and stash him in the bathroom behind you. Punch out the two maids and dispose of them similarly. Final painting by the piano (Painting 3/3).
Corrupt Bonecharm in the bathroom cabinet (Bonecharm 6/7).
Deliliah's cabinets also hide a rewire tool and a bottle of chloroform, bless her twisted heart.
Fifth Floor and up
Duke Abele's Chambers-
A split level penthouse apartment, with a a bath, bed, and servant's room below, and a study with balcony'd bedroom above. Safest to hide fallen guards in the bath area (but be carefully not to accidentally chuck them in the bath itself). The small chamber off the main room (where the real Duke will be held as a madman once you make the switch) has a locked trunk full of treasure. The key for this chest is worn by the Double, and can be stolen from him even after he's become a friendly.
And that should give you all the information you need to replace the Duke with his more affable Double. Once you have, remember to get on the microphone in Duke Abele's chambers for a word with the people. This seems tactically dangerous, since every guard in the city now knows where you are, and everyone who knows the Duke well must know he's been suborned or replaced. Still, you get a special action for it.
The First Floor-
Now it's time to see to the other part of your mission- capturing Delilah's soul. Make for the pantry, down the stairs past the Personnel Only sign.
Two guards chat about relocation- lurk above the breadshelves or on the light fixture in the room outside. When they're done talking, they'll both pass through here. As they head back in, dropstop the trailing blueshirt, then shadow and choke the elite. To the left of the 'Secret Passage' quest marker is a small button, somewhat hidden in the shelves. Press it to open the passage and net a special action.
The pantry also holds both types of elixir, if you've... overextended yourself lately. The passage takes you to a room just outside the vault. Grab the Folded Galvani Resin blueprint from the dining table here (Blueprint 3/3).
Step left to the little memorial to Delilah, and snag the Black Bonecharm here as well (Bonecharm 7/7).
Open the Vault proper with Duke Abele's key. The place is (expectedly) full of loot, including a rewire tool, so don't hesitate to brainswipe the lone clanker walking circles in here.
Also snag the broken gazelle ornament, which you should recognize from Maegan's audiograph at the start of this mission.
At last, approach the central whalebone angel, and bid goodbye to Jessamine's soul, capturing Delilah's. No more spooky psychic commentary on humanity's inhumanity to humans.
Loot the rest of the vault, then return to the Delilah shrine here and smash up the dressing screen to reveal a small boarded up window. Smash through, then use your new, tainted heart to guide you through the flooded passages to the final Rune (Rune 5/5). And with that, we're done with the palace, the Duke, and Karnaca itself. Return through the vault and follow your objective marker to a small jetty near the water below the outer Vault dome. You'll have to swim out to meet the boat, but if you've gotten all the loot you wanted, then clamber on up and skiff on out of here.