The areas of the Cold Casement
(Also yep, Cold Casement the Dark World’s in-universe name.)
Important note! This hinges on my theory about the interior basement door hidden in Asgore’s flower shop.
Lightworld-equivalent map-sketch:
(It's not layed out that way, it's just to get the journey across somewhat. Like projecting the globe onto a flat piece of paper, y'know? Not accurate, but useful.)
Area 1, Interior basement stairs [name undecided]:
Like the purple cliffs at the start of chapter 3. Mostly to be ominous, enable dialogue and to introduce some small mechanics unique to the Dark World. The intro mini-boss fight takes place here. Kris, Susie and Ralsei have to move into area 2, because the rest of the way is blocked by gardening stuff.
Area 2, Corkboards [name undecided]:
A major area, expansive with lots of puzzles. Uses climbing claw walls and strings as ziplines. Has lots of both vertical and horizontal movement. It's a messy city with lots of nooks, crannies and dead ends. You're encouraged to explore.
You have to do some puzzles to progress, but there are a good amount of optional ones too. You encounter the mobile item shop pretty early on. The first puzzle-help shop is there too, and there is an NPC you encounter near each puzzle, which you can use to fast travel to the shop to get help. There's a shortcut door centrally somewhere here, it'll open up later. When you've reached around the end of the area, the mobile item shop will have moved here.
Area 3, Littered floor [name undecided]:
A more linear area, but it has some optional stuff too. A lot of the stuff littered on the floor is car magazines. So it has a car chase/race, think a bit like roller coaster Berdly fight and driving queens car in chapter 2. There's a pitstop in the middle with some helpful optional stuff. Among other things, the mobile item shop has moved here for the time an being. You can also choose to battle the second miniboss here, which will affect the outcome of the car chase/race. A shortcut door will open in the pitstop area later, so you can come back there before you go to the final boss.
Area 4, Desk and drawers [name undecided]:
Another major area and also has lots of puzzles. Area 2 and area 4 mirror each other, they're foils to one another. This area also has climbing sections, some ziplines but not as much. The drawers are the main climbing-mechanic expansion here, moving platforms that can help or hurt on the way to the top. It's also a bit more structured than area 2 in terms of layout, but still has that same exploration focus.
At the beginning of this area is when you encounter the third mini-boss fight, which you have to get though to get to the rest of the area.
Like area 2, you have to do some puzzles to progress, but there are optional ones. The second puzzle help shop is here, and it also has an associated fast travel character. You actually officially get introduced to them in area 3. There's a shortcut door centrally somewhere here, it'll open up later. The mobile item shop will also have two locations that it can show up in here.
Area 5, Exterior basement stairs [name undecided]:
This area is more linear again. Doesn't have that much climbing mechanics, but you get to climb up vines to get up the steps. Each step up has a torch holder, that you can interact with. What happens depends on what puzzles you've solved. In the different areas there were certain puzzles that when you solved them, your reward was talking to a flower, about the size of Flowey that disappear into the ground after you talk to them. They say like one line of dialogue. The one's you've talked to appear again to fill one torch holder each.
You've talked to enough flowers and filled each torch holder, you get access to the chamber that holds the final boss. If you don't you have to backtrack a bit (the shortcut doors open up now that you've reached this area) and solve some more puzzles. The one's that give you flowers are identified pretty quickly by there being some vines present in the puzzle rooms. (But you can also ask an NPC which puzzles specifically, if one doesn't wanna go check and stuff.)
The beginning of this area is the final location where the mobile item shop shows up, so you can stock up on generic healing items before the final boss.
(Btw, just repeating it here cuz relevant: Content regarding the specific areas will be tagged with "area [1-5]" and later also with the area's names when I come up with them.)