*Note this is slightly outdated since version 1.3.
Since the demo has been out for a while and I don't think many people have figured out out how to complete it here's a walkthrough of it.
Spoilers obviously:
1. From the start of the game you wake up in a underground lake. There's a chest all the way to right but you can't get it yet. All you can do is go south until you find a passage that leads up into the next area.
2. The next area is an alleyway with a door you can't enter if you check it. When you leave the alley you'll find a save point. You have to check the Take Items function, you'll find there's 3 weapons and a seabream in it.
3. When you leave the city area there's a large field full of fog you can't see well in. If you just keep going straight you'll see another chest in a graveyard surrounded by block but you can actually break these ones to get 5 matches.
4. If you keep following the path in front of you. You reach a deadend with a save point and a campsite. You can light the campfire with the matches to restore HP when you sit next to it. The campfire can also cook items like the seabream.
5. The building next to save point looks empty but if you check the blocked doors a couple undead break out that you have to kill. There's a bladebug in the corner you have to kill as well which is best done with the rifle since they have very high defense. Killing all the enemies yeilds a an apartment key that goes to the building in the city area with the first save point.
6. When you get back to the city you should save immediately because you won't be able to inside the building. The save room inside has ghosts around it making it unusable, the door across from it has a bunch of pits a couple bladebugs and a TV with static on it. You can knock the bladebug in front of the TV in the pit with a couple shots or if you are carful with the machete. Breaking the TV gives you a 2F key.
7. If you go into the other rooms you'll see one is flooded and has a chest you can't reach and the other has another chest surrounded by blocks, with wyrms sleeping near it. The only way to break the blocks is to use fire magic which the wyrms have, so you need to alert one and let it shoot at you to get the chest which just has money. The gold blocks in the room you have to leave for now.
8. If you go up the stairs there's the 2nd floor which you can enter with the key and the 3rd floor which is open and leads to a statue you can only check for now. When you exit the 3rd floor a ladder appears that leads to the 4th. If you go up to the 4th floor there's more gold blocks in the rooms but if you hit them all they won't do anything, the door in the middle room has to be unlocked first.
9. Going to the second floor there isn't much on it besides enemies, and a room with 4 clocks. Take note of the times on each one. The room with the 3 bladebugs has a pit but if you fall in it you'll just go down to floor below which has the chest in the flooded room. Don't bother attacking the slugs in this room because they will kill you very easily.
10. Back to the room above you'll notice there's some crates around that if you break one the other can be pushed into the pit. If you then fall down the pit the crate will be in the flooded room and you can push it up to the platform with the chest and then jump on it in order to get it. The chest contains an Aurora spell that lets you harm ghost temporarily.
11. You can now use the Aurora spell to attack the ghosts in the save room so you can use the save point. But you still need it to kill some more. On the 2nd floor there's one room that only has ghosts in it that if you kill them gives a chest with a balcony key. Take the key back up to the 4th floor and make sure you bring the aurora with you or else you will have to reload after the next step.
12. Unlocking the balcony you'll see there's a 4th gold switch that has to be hit along with others in the right order, so make sure they are all off before hand. The order is what the clocks earlier where showing you. The hour hands on the clocks point in the direction of each switch that needs to be hit.
13. Once you hit all the switches the gold blocks on the fist floor will disappear revealing a chest but you won't be able to go back down stairs because other blocks will appear blocking the exit to the first floor and the room that lets you fall back down.
14. If you walk around for a bit you'll notice there's footsteps in the background. But before you do anything else go into the room full of books on the 4th floor and get the chest that appeared which contains a taiyaki which can fully heal you. Once you did that if you go into the 2nd flooded room across from there you'll notice you can see where the ghost walking around is positioned. With the aurora spell on you can attack her which you should do using a pistol so she can't hit you right after.
15. The ghost is the boss of the demo named Mizuki. But if you try to fight her she won't flinch much and you'll most likely run out resources before you can take even half of her HP, so your only option here is to run. If you go back to the second floor, there's one room with a large table and some books you can't get by, on the other side is a passage blocked by a cabinet. Mizuki will follow you everywhere once she is attacked and you can bait her into attacking the table so you can get by. Push the cabinet out of the way without letting her hit you and you can go into clock room from the other side.
16. The clock room now has a red switch you can strike only from the side you entered. Hitting it lets you leave the room and opens a passage in the room that only had ghosts in it before. Going through that room takes you into the room with the pit that lets you reach the first floor. You can try and grab the item in the chest that appeared earlier but if you wake up the wyrms Mizuki will put both them and you to sleep with her singing so it's best to wait. You can't enter the save room so for now should just leave the building and save immediately once outside.
17. Once you've escaped if you go anywhere else Mizuki will still be following you but she is less hostile and will only throw fireballs/cyclone spells unless she is attacked. If you go back down to lake area with the first chest you can bait Mizuki into using her cyclone spell to break the blocks yielding an elixer which increases your HP by 100.
18. If you go back to the field and walk back to campsite a character named Satcher will be sitting there who sells items after you talk to him. Unless you did a lot of exploring though you most likely won't be able to buy much, but he does give away a few items for free.
19. The area you have to go to next is a labyrinth hidden in the woods west from the campsite. If you went here earlier you could find a bunch of items that might be useful but hitting the purple crystals will just take you back to the campsite. There's one wall in the south parth of the labyrinth that can only be broken with fire magic. So you nee to lure Mizuki there and have her break it in order to leave the area. One of the harpies in the field tells you about it if you can get them to speak.
20. The next room is an area full of crates which if you break you'll find a potion hidden in the corner. The next room has an alter with a sword in it, but you should leave it for now and just exit the building.
21. Once you leave you'll be back outside near the start where you first entered the city. Go back to the save point and put one weapon away that you don't think you'll need, probably the machete. Make sure you still have at least one full healing item or 3 ideally and then go back to the alter and get the sword. Once you leave with it Muzuki will appear and block the exit forcing you to fight her.
22. Mizuki has 20,000HP and only the Sanzu Blade or an aurora spell will allow you to hit her. The Sanzu Blade you just picked up is obviously the best option to use because of the damage output, if you try using the rifle you can do a lot of damage but unless you found all the ammo it won't be enough to kill her. Mizuki can kill you very quickly in just a couple attacks but she isn't very aggressive, if you stay close enough she won't use her fireball which will force you to dodge and waste SP. If you attack with the Sanzu Blade you can defend if you keep the button held down and she won't be able to do much, but she will eventually change tactics if you rely too much on turtling.
23. The best option I've found is to slide or jump > attack 4x with the Sanzu blade until you run out of SP and need to recover it with a potion. If you get hit too much though you might have to use the potion earlier which will make the fight more difficult but it's possible to beat her without using any other weapons this way, if you get grenades from Satcher they will do 500 damage with aurora on so they can also be very useful.
24. Once she is defeated all the purple blocks in the area will disappear so you can now get the Observer's Stone from the wyrm's room and go back to 3rd floor of the apartments with the statue and place it there. This opens a portal back up to overworld so you finish the demo.
25. You can explore the overworld a bit but there isn't much else to find here right now except some items, Satcher also shows up here near a campsite once Mizuki is defeated.
That's it, I left out how to get a lot of optional items but the demo can be cleared pretty fast if you just follow those steps and you learn Mizuki's attack patterns.