This will be a generic guide on how to get all achievements. I will explain how to get each achievement. I won't explain game basics because you will learn those as you play through the story.
CTRL + F and type the name of the specific achievement you are interested in.

Before we start, let me first explain you how to manually back up saves. This is crucial, soo you won't have to do 10+ playthroughs to have a chance to meet each galaxy. The game gets saved at the beginning of the galaxy, when you visit the Hub and after each Sol.
The save file location is in: C:\Users\*your name*\AppData\Local\Daedalic Entertainment GmbH\HPWIS. If you can't find it, it might be because your AppData folder is hidden. You will need to unhide it, which is done in different ways depending on your operative system. There are 5 files that you need to backup. To go back to the specific point in the story just replace the new save files with the ones you copied.

IMPORTANT: Make a copy of your save files before you leave the galaxy in the following stages: 1, 2, 5, 5 secret, 7(just before you choose cassie or fay), 10. We are doing this so that you can reload the save file and get a different galaxy to explore (and different achievements).

IMPORTANT 2: Research Engine Efficiency until you unlock Engine Power. Max it out and it will increase your ship range by 60%. Without it you won't be able to explore each planet in later galaxies.

• To get this achievement you need to explore all the planets in the galaxy. You will get the achievement once you leave the galaxy and the title of the next one shows on the screen.

• On your first playthrough play normally, explore all the galaxies you encounter and use the remaining Sols on exploring 1 planet to gain further resources and Starch. Make sure to be in the hub when you hit 0 Sol or before (you can head to the next galaxy when you're in the Hub and you have 0 Sols, ignoring the unbeatable boss battle).
  After you're done with the main story, load 1 of the mentioned stages above. Hit 'leave galaxy' and when you get a galaxy that you haven't explored yet, explore it and move to the next one you are missing (it's RNG based so you will have to reload multilple times to get the desired galaxy).

• To access the secret story line you need to explore a special planet that you can get in the 3rd Stage (you will recognize it by it's cream color and a worning sign before you explore it). There's only a 33% chance of you getting it.
  If you're having a hard time getting the secret story line i will provide a download link to my save files of stage 3 with the secret planet. I'm not sure if save files can be transfered between different users. Let me know if the save files work https://drive.google.com/open?id=1cEbXWaOhuCj6zWPxJSmq8YAVcl5EF0EN

Here's the list of achievements related to exploring the galaxies:
Explorer! Curiosity killed the...
Explorer! Sleeping Beauty
Explorer! A Hero's Journey!
Explorer! Raiders of the Lost Quark
Explorer! Who you Gonna Call? PestBusters!
Explorer! Return of the Cheese Heroes
Explorer! Familiar Faces
Explorer! Phantom of the Space Opera
Explorer! Secret Story: Phantom of the Space Opera
Explorer! Pirates of the Carrobean
Explorer! Secret Story: Pirates of the Carrobean!
Explorer! Whale, Whale, Whale! What do we have here?!
Explorer! Secret Story: Whale, Whale, Whale! What do we have here?!!
Explorer! Jail Break!
Explorer! Secret Story: Jail Break!!
Explorer! Familiar Faces...?
Explorer! The Crimson Ruins
Explorer! The Edge of the Universe
Explorer! The Other One
Explorer! Fay Story: Stones of the Ulaya!
Explorer! Cassie Story: Stones of the Ulaya!
Explorer! Dancing with the Devil
Explorer! The Loyal Hound
Explorer! The Unpredictable Doctor
Explorer! The Thorny Rose
Explorer! The Summer Triangle
Explorer! The Final Siege
Explorer! The Dreamers Awaken
The Evil Eye stalks you! (when you complete the secret story line)

You will get this achievement when you collect the Eye of the Kraken. At some point during your explorations you will encounter a shipwreck. Go in, looking for treasure (i believe it's the first option). A battle will follow, at the end of which you will get the eye.

To collect the remains of Fluffy you neet to get an encounter called 'Fay's fluffy'. Choose option (1) "THAT'S MY FLUFFY! MINE!".

Early on in the story, in an encounter you will be asked to pick between a feather or a figurine. Pick the figurine. Later you will get another encounter called 'The honest captain'. Picking option 1 will give you the gold figurine (and the related achievement), option 2 will give you the silver figurine (and the related achievement).

This is related to the Doctor Who encounters. You need to collect the sonic hammer but remember that if you do soo you won't be able to hire Dr Who. During the encounter 'Who', pick option (3) "Hmm... Yeah, i think i do."

This is an item related to the adventure of the cat. In the first encounter, the cat will come across a nest. You have to pick the option that mentions the small birds, option 3 (don't get confused with the option that mentions the nest, that one will give you just 10 starch). This will give you the dead mouse and the achievement.

This is all related to an encounter early on in the game where you have to choose which patamon you pick as yours. The encounter is called 'Wanna be the Very Best' and picking 1 of the 3 options will give you the related patamon.
I recommend option 2, Squirturnip because you will need to win a couple of battles with it to get the 4th achievement 'We are the Champions!', and i know only the combinations of attacks for him.
First fight: Water Spout
Second fight: Aqua Pulse
Third fight: Head Ram
Fourth fight: Snow Storm. If you win the 4th fight you will get the Magenta League Champion Belt and the achievement.

To collect the Jar of Pickles you need to get the encounter called 'We Are (Not) Alone'. Option (3) "Trust Cassie to talk to the two girls and patch them up instead" You will get the achievement and the jar of pickles BUT you won't be able to get the 2 crew members that are related to another 2 achievements.

Rainbow Gem and Sanguine Paragon are story related. In stage 7 Jailbreak (main story) you will be asked if you want to go where Cassie wants to go or where Fay does.
Choosing Fay will get you the Sanguine Paragon in stage 9 The Crimson Ruins.
Choosing Cassie will get you the Rainbow Gem in stage 9 The Edge of the Universe.
At the end of your 1st playthrough reload to Stage 7: Jailbreak and choose the option that will give you the one you're missing. Play again following the other path until you get the one you're missing

This is also story related. In stage 3, after exploring the strange planet that will lead you to the secret story line path, you will get a hard fight. At the end of it you will get the Necronomicon and the achievement.
If you can't get the secret story line i will link the same save files linked in the exploration paragraph. https://drive.google.com/drive/folders/1cEbXWaOhuCj6zWPxJSmq8YAVcl5EF0EN?usp=sharing

In the first 2-3 galaxies you will get the encounter and possibility of hiring her. Pick option 1 ( i think) and you will get a very usefull Craftsmaster and the achievement.

This is related to the encounter in which you get the Jar of Pickles. If you pick option (4) "Ask Azuka and Kyurei about Shunji" you will get both the crew members.

In the beginning of the story line you will get the encounter called 'Who's There?'. Pick option (1) "Spudovah Witnesses maybe?" (Opens the airlock) and you will hire him.

Toward the second part of the story you will get the encounter 'Shades of Red'. Option (1) Crimson gives you Kale, option (2) will give you Tarth Tater.
If you are having a hard time getting this check this thread and the answer by Zero
https://gtm.steamproxy.vip/app/505730/discussions/0/1694919808755133698/?tscn=1650609158#c3278066986679071063
Or use my save files where i got it. Galaxy 8 Familiar Faces (secret storyline) https://drive.google.com/open?id=1YDk02dZbbwDdJhYo8xm7a_ps0ktVkwZ1

In the encounter 'Stray Potato Dog Strut' pick option (1) "He's more then qualified! Let's take him on!".

To get him you need to pick the right option across 3 different encounters
1 encounter 'Who?', option (1) "Uh... Yeah! Of course"
2 encounter 'What?', option (1) "Okay! Where is it?"
3 encounter 'Doctor What' option (1) "Hand him the... Oh."

All of these achievements are related to the research lab. When you max out the research you will get these ones.
This one is not hard at all. In all the playthroughs i did i always maxed them all out. Stark and Sols are plenty.

List of the achievements related to research:
Maximum Efficiency!
Revved up and ready to go!
Just a little bit more...!
Jackpot
Enlightened engineering!
Tank up!
SURPRISE!
Hot iron! Strike it!
Ever ready!
Duct tape salvation!
Everything is under control!
Someone's looking out for ya!
Show me the money!
Fortitude of the mind!
Zombies?! Aliens?! Kaiju?! No problem!
A for effort!
Brainiac!
For Science!
To Infinity and Beyond!
Omniscience

These achievements require you to craft S and SS weapons. Contrary to what you might have expected you actually need to do these in 1 playthrough. If you craft 10 in your first playthrough and another 10 in your second, this won't count. You need to do it all in one.
The hardest one requires you to craft 20 SS weapons in 1 playthrough. During 1 of your playthrough every time you're in the hub look for Craftmasters to hire. A craftmaster is a crew member that has a higher chance to create SS weapons. One of them is Barbie, being a sharpnel craftmaster.
To get the 20 SS weapons craft as much as you can in the galaxies 1-11. We will do most of the
SS crafting in the last galaxy. In the beginning of the 12th you should have 4 craftmasters and around 5 SS weapons already crafted (depending on how lucky you are). Stay in the hub, buy the weapon blueprints and materials. Assign the craftmasters to the weapon they are specialized in and try to get at least 1 SS per Sol. Make a save after each Sol and if you don't meet the quota of SS/S load the previous save.

For reference i crafted 14 SS weapons in the last galaxy, with 4 craftmasters (sharpnel, wave, laser, railgun).

The '50 S weapons' shouldn't be that hard. By the time you get 20 SS you should have already stacked up your 50 S weapons.
Remember that you don't need to keep the weapons in your storage. If you don't need them, sell them but don't loose count of how many you crafted.

List of achievements related to crafting:
Beginner!
Skilled Craftsman!
Exquisite Artisan!
Artificer Adept!
Grand Architect!
Amazing for an amateur!
Keep on rocking, rookie!
Great job, greenhorn!
Very nice, veteran!
Marvelous, maestro!
Hah! A Fluke!
Pfft! Lucky!
Alright, you've got some skill!
You've proven your point!
Fine! You're the best! Geez.

These achievements require you to complete a certain number of explorations. As stated before you need to do these too in 1 playthrough.
To perform 150 Explorations you need a specific playthrough in which you will be exploring 1 planet over and over again. When you run out of Sols, move to the next galaxy and do the same. Don't bother exploring the rest of the galaxy, just dedicate your time to exploring that 1 planet. To make things faster, pick a small and friendly planet (if possible). If you only explore that one planet + do the objectives on each galaxy you will get this achievement by the end of the 9th galaxy.

List of achievements related to planet exploration:
Final Frontier Pioneer!
Extraterrestrial Explorer!
Solar System Surveyor!
Galaxy Trotter!
Inter-Galactic Interloper!

You shouldn't have a hard time getting these. To get all of them you need to defeat 150 enemies. If you play normally and don't waste Sols you should get this in your playthrough.
If you're having a hard time doing this, pick a hostile planet (increased chance of meeting enemies) and large (more encounters) and explore it over and over again. When you're out of Sols, move to the next galaxy and do the same.
Remember that these ones need to be done in 1 playthrough too. They don't carry over different playthroughs.

List of achievements related to defeating enemies:
Veggieslaughterer!
Worldly Conqueror!
Slayer of Solar Systems!
Galactic Gladiator!
Inter-Galactic Warmonger!

You need to do these in 1 playthrough too. You need to complete 100 training sessions. Start working on it from the beginning, Always try to have someone in the training room. Do most of the work in the last galaxy. Once you can no longer train a crew member (and you don't need him) fire him and replace with a new one and repeat the process until you have your 100 training sessions.

List of achievements related to training:
Here we go... !
Blood, Sweat and Tears!
Queens of Pain!
Tyrant!
Task Mistress!

That's all the achievements. They are not particularly hard, just time consuming. If you 'save scam' you won't be sinking as much time as i did into this game. To get a different galaxy i started a new game each time and hoped to get the one i needed. I played this game 6 times and only in the end found out that you can save previous to the galaxy that you're missing and reload if you don't get the desired one.
Anyway... good luck achievement hunters!