I made this guide with the help of people providing information in the comments as the dlc just came out, when there were no other guides. I'm gonna leave it as it is for now, but please check out the comments if you still have any questions!

You can also add me and I'll try and help personally!

Find the hidden korok/golden poop.

This is located in the Dream World and can be accessed through the fire in the Hidden Gorge. Once there, go turn off the torch that opens the door to the Forbidden Archive and then head back into the main building. A door has been opened to a staircase that leads to the top level of the building. There you can jump over the railing and get on the roof. Get to the top of the roof and there awaits your prize!

Speedrunner Nepo has made a guide on how to get this achievement on their youtube channel here:
https://www.youtube.com/watch?v=JVLEJaA-KEA

Information provided by Genome & Nepo

P.S. I realized after reading Windoki Tarot's guide on how to find this that the golden poop is only visible while not carrying an artifact when finding it LOL
So I've updated the description to "Find the hidden korok/golden poop". This achievement is a reference to The Legend of Zelda: Breath of the Wild where finding 900 korok seeds reward you with a piece of golden poop.

Complete a full lap around the Stranger in 90 seconds or less.

This can be done easier when the Dam is broken since water levels are higher and the water is moving faster.

Burn a Slide Reel in a fire.

This one is very straight-forward. Just bring a Slide Reel with you to one of the green fires and put it in the fire.

Information provided by clemendo35

Bring a prototype artifact into the Dream World.

The prototypes can be found in a box in the Damaged Laboratory accessed through a hull breach on the outside of the Stranger.

Information provided by DJ Fennec☾✰

Shoot your scout at the "Sun" of the Stranger, which looks like a big light-bulb and is attached to the window facing the sun.

This requires some precision, and can be done easier at a higher altitude, for example the top of the tower at Cinder Isles.

Information provided by clemendo35

Get crushed by an elevator on the Stranger.

This can be done in the Dream World as well and is recommended if you don't want to restart the loop from dying.
Also, I couldn't get this to work with the elevator in the hangar that leads to the Dam since I just clipped through it.

Information provided by clemendo35 & DraconisEltanin

Reach all three Forbidden Archives in one loop without getting caught.

This one is a bit difficult. But once you know the means of getting to the Forbidden Archives it's just a matter of doing them in the right order and quickly.

Here's a great guide with a route made by rat baby!
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=2615013749

Get caught by a pursuer in the Dream World while not carrying an artifact.

You can place your artifact on the ground when you're in the Dream World.

Information provided by KayKay

Bring an artifact to a normal campfire and doze off.

Any normal campfire should work for this, although it didn't work for one person at the newly added campfire next to the radio-tower.

Information provided by clemendo35 & PkPenguin

Get woken up in the Dream World in 5 different ways during a loop.

Apparently some people have had issues with getting this achievement, the following ways of waking up was what I did to get it, but if it doesn't work for you I recommend just trying any other way that you can think of, and even the same ones again as one of them might not have registered properly. You should get this achievement eventually after enough tries.

The ones I did was:
Standing in fire, Fall damage, Falling into water, Caught by pursuer and Awoken by the bell

Information provided by clemendo35

Go through one of the Dam's Water Outlets.

The outlets are located at the bottom of the Dam, so you have to swim down while the Dam isn't broken and then just simply go through.

Break the Deep Space Satellite.

Just nudging it out of its orbit isn't enough. Ramming your spaceship into it at full speed is enough.

Ride the wave on a raft for 15 seconds.

Some tips on how to do this:
Don't start at the Dam, since the size of the wave at the start will most likely knock you off your raft. Make sure there's not a lot of obstacles and a straight path ahead before you attempt this, a good place to start could be the Cinder Isles.
You can also use downwards thrust while on the raft to help you stay on top of it.
The Dam breaks around 13 minutes into the loop, so dozing off at the campfire at the start until about 10:00 or 10:30 minutes into the loop should give you enough time and will make the process of attempting this achievement easier.

A tip on how to do it from Shirleehee:
"For Tubular I positioned my raft right past the natural stone archway separating the first little town from the second. Then when the dam broke, I tried to force my raft to the leftmost river and just coasted that as far as possible. I slammed into the rocks where the electrical cables are and got the achievement."

Here's two videos showing this achievement being done, made by Imaria & Zambies:
https://youtu.be/AhUI6RbSX1g
https://www.youtube.com/watch?v=2MCpru_7jwI

Information provided by Shirleehee, Babar, Mr. Beartato, Zambies &
Imaria

Jump to your death to escape your pursuers in the Dream World.

This achievement seems to either suffer from a bad description or is just bugged in most areas.
You seem to be able to be reliably get this achievement in the area of the Dream World entered through the Hidden Gorge.

Once you've entered, start by extinguishing the torch that opens the door to the Forbidden Archives and then go back to the main building. Go through the area the intended way until you reach the totem that you need to light to make a bridge across the big room with the staircases. Then instead of going back the intended way with the help of the hand statue, simply jump off the railings to your left into the water.
The achievement should unlock after this!

Here's a video made by Babar that shows the steps:
https://www.youtube.com/watch?v=7l2n8klKUus

Information provided by RobotSheepy & Babar

Thanks again for all the contributed information!
And also thanks to those who gave my guide a reward! This is the first guide I've written and I tried my best to make it easy to follow!