The first two can be done together since they have a common ingredient, the life Tonics (that give you +1 max health) some characters give you after you help them. The others will also be completed while you gather those Tonics.

The first step is gathering the Life Tonics (corrected as suggested by awg):
1 - Strike Leader: Find the snake and save it. If you have Timothy you can use his Quantum Tunnel ability to get the right location card. This is the 1st Tonic.
2- The Prisoner: With Karst on your team, in the first zone, the frog merchant, Gribbaud will give a mission to deliver a package, completing it will grant you the 3rd Tonic.
Before delivering the package, inside the prison, you can save the snake again and it will give you the 2nd Tonic.
3 - The Negotiator: Finish the mission just to get Isabelle and prevent the attack of the Militia.
4 - The Rescue: With Karst on your team, search 3 abandoned docks. They can be found after Looter’s ambush with Listening Ear. You should have 4 Tonics by now.
5 - The Escape: Buy the Raft from Gribbaud (you can use Isabelle to lower the price), making a deal with the merchant is necessary to get a tonic later. In the third zone choose to go through the river and look for the snake card before completing the zone, saving it will grant you the 5th Tonic and the “You sssaved me” achievement.
6 - The advocate
7 - The Herbalist: In the last zone capture Hector alive by using a claw trap during combat while having all the other zones illuminated (showing a location instead of being dark, even if they have monsters), otherwise he will escape. You can use Timothy to get the right card from the deck. This will be the 6th Tonic and will grant you the “Gotcha” achievement.
8 - The siege / Blocade- You will arrive one turn late so the mission should be The Siege instead of the blockade. You just need to finish it.
9- The Nymphant - First make sure you gather a lot of Cooks, depending only on the skill card from Pattenbois or Isabelle might require resting too many times.
In this mission, look for the Gribbaud card after visiting the tomb, he will give you the last Tonic. In my run, I missed one of the others and this was my 6th.
Once you have the 6 tonics use the Cooks or the skill cards to mix two tonics and get a potion that gives you 3 max life instead of 1, repeat this 3 times and you’ll have a total of 9 max life you can use on Timothy to reach 18 and get the “Invincible” achievement. Lose the game or restart the mission to do the other achievement.
The “Force of Nature” achievement is similar but besides the Cooks you’ll also need Spores. I know they can be found in this level. Mix a Tonic of Life with Spores and you’ll gain a new potion that increases the attack power, do this 4 to 6 times to get enough potions. Even 4 or 5 might be enough if you use skill cards during combat, one for the character you upgraded and the Battlecry skill from Karst that you gain for saving all the miners in The Rescue Mission.

23/09/2024 - UPDATE suggested by Nyko, check the comments below since I can't fit it here

For the first achievement you just need to complete The Negotiator mission.
For the second, you need to get the Deal Breaker skill. After completing The Negotiator, go to The Prisoner mission. I’ve read that having Timothy with you will force you to restart if you give away the real Lyre, so what I did was make a new first run in another save slot. Maybe the ideal solution is completing this achievement first when you start playing. In The Prisoner mission Gribbaud will give Isabelle a delivery mission, similar to the one he gives Karst. Just pick the package, don’t open it and deliver it in the third zone, in the guard post, after defeating the guards and using Collect Debt to call the messenger. After this you’ll have this new skill.
To get the achievement you’ll need to find an enemy with 4 or 5 life. The bandits that throw firebombs are the ideal candidate and can be found in The Rescue mission, but before facing them you need to lose some life points first. After this, in the battle screen use food cards to increase the damage of Isabelle’s skill fist, and then use it on the enemy. I tried using just skill/resource cards but after the third card, combat starts right away.

For one or both achievements you need to have completed “The Bad Place” Ending (just follow all the cultist missions until the end) and visited the Forbidden Library to discover the Cure, I didn’t try to mix Spores and the Blue Algae before completing the mission but it might still work.
The main difference between them is not having Morin Khuur from The Rescue Mission. If you don’t have it, you’ll get the Medium Place Ending. This ending apparently also doesn’t need all the companions, but it’s better to still get them all to train for the Good Place ending. Also, Timothy will prevent you from leaving The Rescue Mission without the Artifact so you’ll need to play it without him.
IMPORTANT: The Good Place should be the last achievement you get, after getting it the save slot gets blocked and can’t be used.

For both, just follow this order for the missions:
The Strike Leader (recruit Karst and recover the address of the Forger)
The Negotiator (copy the Lyre and give the fake to Lady Katell, recruit Isabeau)
The Rescue (save Volepain's father and recover the Morin Khuur)
The Advocate (recruit Pattenbois)
The Herbalist (recruit Sylvia and don’t kill or use dread too much or she will leave)
The Blockade (confront and kill Ink Blood to prevent Isabeau's assassination)
The Liberator (craft the cure and give it to Volepain, free Leo and recruit Aube)
The Sacred Temple (recover the Lute of Origins)
The Weaver (perform the ritual to save the world, you will need all the characters).
Reaching this last mission will grant y

Just stockpile 20 points of fame in The Herbalist mission, before reaching the hostage situation. Making enemies retreat, interacting with the bard or giving food are the best options to gather fame. Once you reach him, just spend the 20 fame instead of fighting him or using the “The Tome is Elsewhere” card.

Reach The Alliance mission and pick Isabelle.
In the first trial, just use acid on the chains to get It’s not cheating”
For Double Trouble you just need to defeat the brothers without fighting them. Start a fight in the tavern by using the pepper cloud, this will draw them out, then you need to get acid for the one with the armor and rum for the other.
After defeating the brothers, continue exploring until you see a card being replaced with a similar one but with tentacles, use one of Isabelle’s skills to start the fight against Ink Blood. Using the objection card you get from the perfect trial will make it easier. After defeating him you will get the “Squid Game” achievement.
Later, in The Siege mission, the enemy captain on the Calamar won’t be Ink blood but another, defeat her and you’ll get the special weapon and the ”One Shot Blade” achievement.

Reach The Nymphant mission with Timothy on your party and meet Lum (they are bothers).

Just follow the Cultist’s missions and in the end you can choose not to save your companion that gets taken as a hostage by Rainier. Doing this will grant you the first achievement. Finish the rest of the mission to get “The Bad Place” and when you start the game again Timothy will reveal his real identity and you’ll get “Super Moth boy”.

Get the Forger location map from The Strike Leader mission and after that go to The Negotiator mission and give the fake Lyre, this will grant you the “Blind as a bat achievement. To get the other achievement you need to follow the Cultist’s missions but they might be locked if you already have Timothy. So either complete this before the bad ending or start a new save slot.

This can be completed on several different missions, just pick Timothy and use Mesmerize on the Bard, then he will play the dirtiest song ever.

In the Rebellion mission, don’t kill anyone. This is easy to accomplish, you just need to stockpile resources and use Timothy and Isabelle, since both have skills that demoralize the enemy and win fights without spilling blood. This will also grant the “Gorilla Warfare” achievement.

Spending 10 coins is easy, but you need a strong enemy party that lasts more than just one turn. I gained it by spending coins on Rainier but you can also do it against bandits or guards.

Reach the Nympant mission and find Noctomoth's Tomb by using the Pilgrim or Bird’s nest on the Infected Jungle. Reaching the tomb twice will grant the achievement. I did this in two runs but apparently it also works in just one.

For the first achievement, just complete The Advocate mission.
In this same mission, you’ll need to gather this cards for the perfect trial afterwards:
1- Barkeeper or Sailor witness: In the tavern, use the listening skill to reach the hideout. This will get you the kill list evidence and will distract the barkeeper, steal the wooden leg from him and return it to convince him to be a witness. You can also use Timothy’s “mesmerize” and keep the leg. You can also get a Sailor Witness from the docks.
2 - Use Volepain’s solidarity card on the poor neighborhood to find the Block Kids and get one of them as a witness.
3 - Find the Nobles in the Noble District and get one as a witness.
4 - Find the city watch, they will give you information about the crime scene and add it to the deck. Buy a tracker from them to use on that crime scene, after a few combats you’ll reach the witness. He will ask for a bodyguard (assassin, thug or mercenary, all work) before accepting to be a witness.
5 - For the evidence, you’ll need to open the package you get in the first zone and the kill list from the hideout.
In the trial itself, use the barkeeper or sailor on the dock’s worker, the kid on the second jury member and the noble on the last one. Then, use the kill list on the Judge, then the scared witness testimony and lastly the ink bottle. I think the order of at least the first two items probably doesn’t matter, but I used this order anyway. This will grant you the objection card and the The Pelican brief achievement.
To get the Trial by Combat achievement you just need to botch the trial and use the pepper smoke on the guards to start a fight.

I got this achievement in the Temple while having Aube, Isabelle and Volepain.
You need to find an enemy party of 6 enemies, preferably strong ones. You can spend food or use the smoke ability to get rid of the weaker ones, while leaving the strong ones for last. Then, you can use food again or Aube skill to recruit them for you. Having Isabelle on the party helps reduce your damage and avoid killing enemies in the first round of combat.

Reach The Escape mission with Isabelle and choose to go through the forest. Then, use Call for Help and you’ll notice that the usual envoy got ambushed by bandits. Defeat them and you’ll get a better Call for help, use that card and you’ll get the ”Stronk” achievement.

As I already mentioned, this guide uses a lot of info that Lucanael and CeirahMoon already posted, I only made it to make the information more clear and easier to follow.
I hope this guide helps.