This guide is a work in progress. It is not complete yet. I haven't gotten 100% myself.
Help is much appreciated, doesn't matter if from the dev(s) or other player(s).
EDIT: The devs abandoned the game and so I did the same with that guide as I couldn't figure out how to get some achievements. Some may be bugged too.

I also made a separate guide for both trust achievements and the sidequests:
https://cs2bus.com/sharedfiles/filedetails/?id=2061889640

What I miss, think is bugged or just open questions which means these are the points I could need help with:

• Collectibles: I am missing one pennant, though I collected a pennant which doesn't register properly (seen in the PDA; tried multiple times). Is it bugged or is there another pennant?
  EDIT: checked every room multiple times, I can definitly say there isn't another pennant, so this achievement is bugged.
  So, for anyone who wants to know: this is the pennant not registering:
  
• "Tour de Kursk"- Achievement: I am sure I was in every room (in four different playthroughs !!!), still didn't got achievement. Has to be bugged except there are secret rooms, but I highly doubt that. Also you can't enter section 7, but if you approach the door, you can see a dot there. Are you supposed to go in there somehow? Do only the rooms count before the incident takes place?
  
• "All Alone"- Achievement (aka Ending 1): No idea how to get this. A lot of people said by getting lowest trust. Though I did that and still didn't got Ending 1 at the end.
  So what is supposed to happen in this Ending: "Robert opens the hatch, tells you that it was all your fault (you have negative influence), and closes it. This results in your death." (said a dev)
  
• The one soldier at the port giving you the code: 483. He says that he hide some cigarettes and goodies in one of the lockers by the sauna. So I guess he meant the locker room? But I couldn't interact with those (except for the story mission). How does this work?
  
• What is the point of making photos? (except the one photo at the truck which gives you an achievement) I assume that there is no advantage of taking photos.

You don't have to worry about those as you automatically get them while progressing through the story. Though I won't tell you how to do that as this isn't really hard and there are also enough walkthrough videos on Youtube.

• Moscow
  
• Vidyayevo
  
• All Aboard!
  
• Ready for Combat
  
• Going for a Swim
  
• One of Us
  
• Mind the Walls (By playing the Tunnel minigame. You actually have to play this game for the story, also I did get the achievement before reaching the needed score.)
  
• Happy Birthday!
  
• Data Thief
  
• A Little Poem
  
• Shkval Torpedoes
  
• Silent Hunter
  
• Lockpicker (this also marks the point of no return !!!)
  
• End of a Story

I will try to guide you here from one collectible to the next. I will also tell you every room even if it is empty because of the "Visit all available rooms"- achievement. You can also check your status of the collectibles on your PDA, because they are treated as sidequests (except the Matryoshka).
Achievements related to collectibles:

• Scribe for all the letters and notes (there are 3 notes which don't count for the achievement, so they are optional)
  
• Matryoshka for the only Matryoshka
  
• Pennant Enthusiast for all the pennants
  
• Collector for all the collectibles (which does include notes (18), pennants (16) and models (4))

I am missing one pennant, though I collected a pennant which doesn't register properly (seen in the PDA; tried multiple times). Is it bugged or is there another pennant?

So let's start:

• At the intro is a note on the table WHICH DOES NOT COUNT!
  
• Nothing in the hotel room.
  
• At the port: Go on top of the right crane, there is a note on the ground.
  Before entering the Kursk, there is a pennant to the left.
  
• Then proceed till the Kursk dives down. From now on you can visit most of the areas of the Kursk and collect most of the collectibles. (All collectibles except two notes and one optional note.) Also you can collect them in any order if you want.
  In the commando room (where the captain is), is a pennant.
  Go in the little room connected to the commando room. There is a note.
  
• Go down the ladder and through the door. You are now in section 2. There are 5 doors here. First take the only door on the right. You are in a bigger room. From there access a little room with a note inside.
  Now go back two doors. From there take every door on the left (4 doors). You find only one collectible: a note in the last room.
  
• Take the ladder down in section 2. A note and a pennant in the first room (computer room).
  (Another note there you can't pick up now. Don't worry, we'll pick it up later.)
  A pennant in the second room (have to lockpick it).
  Third room is empty. Now go through the last door and the next door. A note is there.
  
• Now go back up the ladder and go in section 1. Nothing in the big room, go down the ladder. A model and a pennant there.
  Go through the only door and through the next door. Nothing there.
  
• Go back to section 2 and enter section 3. There are 5 doors here. Go through the only left door. A note in the left corner WHICH DOES NOT COUNT for some reason!
  Go through another door, empty. Go back and take the ladder up. A model is there.
  Go through the only door, empty. Go back to the 5 doors. Take every door on the right. Behind second one (have to lockpick) is the matroschka.
  Behind third one is a note.
  Behind fourth one is a pennant. (!!!THIS ONE DOES NOT COUNT!!!)
  

• Now go downstairs. A lot of doors here. A note behind the first door you see.
  From that room turn right and take the last door. A note is there.
  Go back, past both stairs and take the last door. A pennant is there.
  Lastly go through the metal door, a pennant is there.
  Downstairs is nothing, same with other room here. Go back where all the doors are, go downstairs and lockpick the only door. A pennant is behind it.
  
• Go back up two sets of stairs and enter section 4. First check the doors on the right, the first two doors can't be opened now. Only in the sixth room (have to lockpick) on the right is a collectible: a note.
  Now go back and take the first door on the left. Two notes and a model there.
  Go through the door, a note is there.
  From there take the left door. A pennant is there.
  Go through the door, go back to the entrance of the section and go downstairs. The three rooms opposite the stairs are empty. Take the door right after those (the medical room). A pennant is there. Next little room is empty.
  From there continue on and find a note in the locker room.
  In the staff room is one pennant to the right and one to the left.
  
• Now back up the stairs twice. Turn right and go through every door counter clockwise. First three doors are empty. Fourth room has a pennant.
  Next four rooms are empty. Now through door next to the stairs, there is a note.
  Go out again. On the left wall is a pennant.
  Now take the last three doors here. In the first room is a note on the bed, hard to see.
  Next room is empty, last door can't be opnend.
  
• Now go in section 5. Both doors here you can't open, so go downstairs. Both rooms here are empty. You can enter section 5-bis here. Ignore it for now. Go downstairs. The three rooms here are empty. Go down the ladder. A model and a pennant are here.
  
• Go back up twice and enter section 5-bis. The room on the right is empty. Go downstairs and lockpick the only door. Room is empty. Back upstairs and up the ladder.
  
• From here enter section 6. Go through only door and through both hatches, in each case go down the ladder. All empty there.
  
• That's it for now. Progress through the story. You will naturally come into those rooms.
  
• In the captain's quarters is a note.
  
• A note in the computer room you couldn't get earlier. Need to make the guy leave the room. (After the "Happy Birthday!"-Achievement)
  
• Same note as in the intro. THIS ALSO DOES NOT COUNT!
  

• A True Classic: Get a score of 550 in the PDA minigame. (At least that was the score which granted me the achievement.) To play it, press "TAB" to open the pda, now choose the third symbol to play the minigame. It is basically snake.
  You get the achievement while you are still alive.
  
• Target in Sight: You have to achieve a score of 65 in the Periscope minigame.
  (At least that was the score which granted me the achievement.)
  You get the achievement while you are still alive, I think.
  
• One more?: You have to play the board game in the staff room once. (Not sure if you also have to win it. But better win I guess.)
  
• Biker: In the staff room you have to beat every rekord on the bicycle ergometer. These are quite a few. So you have always one minute to break a rekord. After everyone you beat, it gets harder. But still it's not that hard.
  
• Too Fast for You: Achieve the top score in Flashout, located in the staff room. There are two games called "Flashout". Check the pics to figure out which one is the right one. You get the achievement after you run out of lives. Though I am not sure how many points you need. (Maybe the score isn't even important for the achievement?) When I got it I had about 41k points. BUT
  !!! THIS ONE IS DEFINITLY PARTIALLY BUGGED !!!!
  Because I had a run where I got about 68k points, died, but didn't got the achievement. I suggest you to do the following if it is bugged for you (without guarantee that it works): go in your saves folder (located here: C:\Users\your username\AppData\LocalLow\Jujubee\KURSK\76561198043693378), backup your saves, then delete them, start a new game, try the minigame now.
  
• From The Deeps: Achieve the top score in Shmup, located in the staff room. You can see that on the console it is written "Flashout". But this is false. See pic. You get the achievement after you run out of lives. Though I am not sure how many points you need. (Maybe the score isn't even important for the achievement?) When I got it I had about 11k points. BUT
  !!! THIS ONE IS DEFINITLY PARTIALLY BUGGED !!!!
  Because I had a run where I got about 430k points, died, but didn't got the achievement. I suggest you to do the following if it is bugged for you (without guarantee that it works): go in your saves folder (located here: C:\Users\your username\AppData\LocalLow\Jujubee\KURSK\76561198043693378), backup your saves, then delete them, start a new game, try the minigame now.
  

-First Secret: At the port, before going into the Kursk, you have to get your Survival Kit. After you do that, push the box away, move to the other side of the truck, lockpick the little box, then make a photo. Be aware that there is a guard patrolling there. If he sees you, you loose and return to the last checkpoint. So the best is to wait until the guard just leaves the area before the truck, then lockpick.
(To be able to make a photo you have to first zoom in by holding "W", then press "E" for the photo on the right spot.)

-Favor For A Soldier: Also during the port section. Speak with one soldier which is at the right corner sitting on a box. Say that you will bring him some cigarettes. Then go to the guy just before the entrance to the Kursk. You can ask him about cigarettes and he will give you some. Now go back and give them to the soldier.
(He will also give you a code: 483, but I have no clue for what this is for.)

-Hacker: Have to hack all 3 computers. This achievement is technically missable, though very hard to miss. You HAVE to hack two out of the three computers during the story. The hacking itself is not difficult. I am sure you will figure it out. Also the codes are random. The locations for the computers are as following:

• the computer in the captains quarters (the only one which is not mandatory, though you have to go in the captain's quarters.)
  
• the computer you get access to after you get the "Happy Birthday!"-achievement (mandatory)
  
• the computer in the sonar systems room (mandatory; you can get caught hacking this one!)

-Tour de Kursk: Visit all available rooms.
Didn't got it yet, though I tried my very best. I think it is bugged.

-Who Is He?: Gain the lowest Trust among the crew.
To do that, always (or nearly always?) answer rude, selfish and arrogant. Try to accept as many sidequests as you can without finishing any in the right way. A few of them can be failed, do that. Another one can be refused, do that too.
For a more in depth guide check this one:
https://cs2bus.com/sharedfiles/filedetails/?id=2061889640
This achievement pops up as soon as your trust level (can't see that anywhere) is below a certain value. If you follow my guide you get it during the talk with Alexey (he engraves the flask).

-Our Brother: Gain the highest Trust among the crew.
To do that, always (or nearly always?) answer polite and helpful and do all sidequests (of course the collectibles-sidequests are optional for that). I also talked to guys which only give one sentence of monologue, don't think it is necessary, but who knows.
For a more in depth guide check this one:
https://cs2bus.com/sharedfiles/filedetails/?id=2061889640
This achievement pops up as soon as your trust level (can't see that anywhere) is over a certain value. If you follow my guide you get it during the talk with the medic guy almost at the end (it is before you can open the safe of the captain).

-Sharpshooter: At the ending sequence you have to shoot at one point at a fire-extinguisher. Later on choose to find the hole in the hull (see Ending 2/3). Then you will have to shoot at a lock.
To get this achievement, simply don't use all your bullets. It seems you have 4 bullets, which means you can only miss once. But it is quite easy.

-Patient: Watch the credits till the end

-A True Marine: Get every other achievement

-All Alone: Ending 1: No idea how to get this. A lot of people said by getting lowest trust. Though I did that and still didn't got Ending 1 at the end.
So what is supposed to happen in this Ending: "Robert opens the hatch, tells you that it was all your fault (you have negative influence), and closes it. This results in your death." (said a dev)

-Together In Death: Ending 2: One guy at the end will ask you if you want to follow him or if you want to find a hole in the hull. Choose to follow him.

-Survivor: Ending 3: One guy at the end will ask you if you want to follow him or if you want to find a hole in the hull. Choose to find the hole. You will eventually make it out of the submarine. Now swim up to the surface.

-Faint Hope: Ending 4: Same as Ending 3, but don't swim up. Instead wait outside the submarine till you drown.

-Seen It All: Get all Endings

Here I give credit to everyone who helped me in this guide. Thanks to all of you!

• 7UC4 C4551N3771
  (helped with A LOT of things, like Endings and Minigames)
  
• Arctica
  (helped with some general stuff here and there)
  
• LickAnusHappyFallus
  (helped with one collectible I couldn't find and we also discussed a lot of stuff for the game)
  
• RezavejTank
  (helped with some advices for the "Who Is He"- Achiev)