This achievement occur totally in space, so we are not gonna land, so no expeditions, so no necessity of many crewmates. I usually go with Emmet + April. Emmet have a good skill about getting extra material from events, and without expeditions, soup became more scarce and we need all the materials possible.

To keep you from starving in space, just keep building Communicators, upgrade it, recycle it, make 3 Soups, recycle 1 Soup, make a Communicator... and the loop continues.

Remember, the tape solves almost everything and do not eat the cheese!

Liberté, Égalité, Tomate
Reach all endings featuring Captain Félicette.


Number of Endings: 4/4 - Agree in sharing some customary drinks with Captain F.

NOTE: I am not sure what triggers Ending 1 or 3 to happen, for me it was inconsistent between runs, so maybe you are bound to one since the beginning.

@Doloeri comments: I got the impression that to get the Earth ending with cats you need to fail as many times as possible (similar to the dog story). I agreed to help the cats, helped with the first mission, failed the second, agreed to take the cats on board, didn't help them on board, helped in the final mission when Felicite said it was critical. Got the Earth ending twice this way.
Leave a comment if you can confirm it!

Ending 1: Joined the French Feline Space Section and colonise a planet.

• Can I count on you in the future? -Yes (if you say No, you will never see them again)
  
• Here you will randomly get events to help the cats (Seems anything besides Nothing, works)
  
  • Chain 1: Could you assist us in some manner? -Tape
    
  • Chain 2: We are dying for some merriment. Will you assist? -Armor
    
  • Chain 3: Until there is sand, we cannot got. Please, monsieur, can you help? -Handbook
    
  • Chain 4: Help us monsieur. Before we are consumed by this vacuum madness! -Artifact
    
  • Chain 5: Is she a cat, and how she can truly know? -Handbook
    
  • Chain 6: Help me, for I can feel my will breaking as well! -15 of Energy
    
  • Chain 7: She is trying to make fetch happen. -Battery
    
  • Chain 8: An amusing request. Why aren't you laughing, sir? -Agility
• Here you will have a random visitor in your ship
  
  • Chain 1: Bring Monsieur Latte to our ship. A fabulous idea, yes? -Yes
    
  • Chain 1: This thing is of interest to me. Will you give it to me. -Tape
    
  • Chain 1: The questions is, what are you gonna do about it? -Nothing
    
  • Chain 2: Two of my compatriots are en route to you right now. Should I open, Captain? -Yes (I got this one in my run)
    
  • Chain 2: Care to... assist? -Not Nothing
    
  • Chain 3: May I introduce to you my two trusted officers. May they board, monsieur? -Yes
    
  • Chain 3: Please, sort this out. -Soup
    
  • Chain 3: Where is she going now? -Intelligence
• Here will appear one of the previous random events, give them something
  
• Would you like to join us, monsieur Captain? -Yes

Ending 2: I LOVE CATS, I LOVE CATS, I LOVE CATS

• Same as Ending 1 but at the end:
  
• Would you like to join us, monsieur Captain? -No

Ending 3: You and your allies from La Véronique voyaged back to our home planet.

• Seems everything is gonna be the same as Ending 1 until the very end, seems to be random, I did fail one event here tho (Read the NOTE at the start)
  
• Would you like to accompany us back home? -Yes

Ending 4: Your ship became an huge litter box

• Same as Ending 3 but at the end:
  
• Would you like to accompany us back home? -No

Man's best comrade
Reach all endings featuring Commissar Laika.


Number of Endings: 4/4 + 1 - Pick up the unknown hitchhikers to start this chain.

Ending 1: Joined the space crime canine gang.

• Throw me a bone, will you? -Shovel or Battery (you will lose it). If you choose Nothing, Laika won't contact you again.
  
• Now it is going to appear 3 (or 4?) different events in random order, if you don't help them 2 times in a row, Laika won't contact you again.
  
  • Chain 1: You gonna pick 'em up or not? -Yes
    
  • Chain 1: You could confront her, of course. If you dare. -No
    
  • Chain 1: It's probably now or never -No
    
  • Chain 2: Is she really coming aboard? -Yes
    
  • Chain 2: I'm giving you a best friend discount, since we are so close. Interested? -Soup (you will lose it)
    
  • Chain 3: Will you let Laika's comrades on board? -Yes
    
  • Chain 3: Surely you have universal healthcare on this ship? -Shovel
    
  • Chain 4: Fancy giving us a paw, then? -Yes
    
  • Chain 5: So... any ideas, comrade? -Artifact (you will lose it) (not sure what would happen if the 30 of minerals are given)
    
  • Chain 6: Can you do that, for the galaxy? And also, for me. Spasiba. -Intelligence (not sure what would happen if Strength is chosen)
    
  • Chain 7: Ready for some tomb raiding? -Shovel
    
  • Chain 8: Got a package need delivering. Simple, da? -Agility
    
  • Chain 9: Maybe we'll even let you try it out, yeah? -Tape
    
  • Chain 10: It's not even locked, just need to open up the lid. -Strength
    
  • Chain 11: Fast and discreet, before robopatrols get alerted. Da? -Agility
• We're leaving this galaxy. Wanna come with? What do you say? -Yes
  
• Join us if you want, and bring your human comrade. And some of that delicious soup, da? We're running out fast. -Soup
  
• If you handle this well, maybe it can fly under the radar. Figuratively. -Higher one (if you fail here, there would be another check, if failed you will get the Ending 2)
  
• You can't be in two places at once! Isn't that what crew is for? -Crewmate (both seems to work, not sure if you can fail)
  
• It is a total space engine jam! What do we do? -Choose the one more prone to success and hope for the best.

Ending 2: You and your crew were left on a tiny, forsaken space rock.

Follow the Ending 1 until the next input:

• We're leaving this galaxy. Wanna come with? What do you say? -No

Ending 3: You were taken hostage aboard their own ship.

• Throw me a bone, will you? -Shovel or Battery (you will lose it).
  
• Now the idea is to accept the events but botch them:
  
  • Chain 1: You gonna pick 'em up or not? -Yes
    
  • Chain 1: You could confront her, of course. If you dare. -Yes
    
  • Chain 1: It's probably now or never -Yes
    
  • Chain 2: Is she really coming aboard? -Yes
    
  • Chain 2: I'm giving you a best friend discount, since we are so close. Interested? -Not the Soup
    
  • Chain 3: Will you let Laika's comrades on board? -Yes
    
  • Chain 3: Surely you have universal healthcare on this ship? -Nothing
    
  • Chain 4: Fancy giving us a paw, then? -No?
    
  • Chain 5: So... any ideas, comrade? -Nothing
    
  • Chain 6: Can you do that, for the galaxy? And also, for me. Spasiba. -Strength
    
  • Chain 7: Ready for some tomb raiding? -Gun
    
  • Chain 8: Got a package need delivering. Simple, da? -Strength
    
  • Chain 9: Maybe we'll even let you try it out, yeah? -Tape
    
  • Chain 10: It's not even locked, just need to open up the lid. -Nothing
    
  • Chain 11: Fast and discreet, before robopatrols get alerted. Da? -Gun
• We're leaving this galaxy. Wanna come with? What do you say? -Yes
  
• If enough events were botched, on the heist day, you will get this ending.

Ending 4: You and your crew were left on a tiny, forsaken space rock WITHOUT SUPPLIES.

• Do same as Ending 3 until:
  
• We're leaving this galaxy. Wanna come with? What do you say? -No

THIS LAST ENDING DOESN'T COUNT TOWARDS THE DOG ACHIEVEMENT
Extra Ending: You ended captured and sentenced to a lifetime of soup mining labor.

Follow the Ending 1 until the next input:

• If you handle this well, maybe it can fly under the radar. Figuratively. -Choose the one more prone to fail, then you can choose a crewmate, choose the more prone to fail too and you will get this Ending, but if you success (yay?), you have another opportunity.
  
• You can't be in two places at once! Isn't that what crew is for? -Crewmate (both seems to work, not sure if you can fail)
  
• It is a total space engine jam! What do we do? -Choose the one more prone to fail and fail.

Unidentified Flying Offspring
Reach all endings featuring the UFO.


Number of Endings: 5/5 - Share source data with the UFO A.I. to start this chain.

Ending 1: The UFO graduated with honors from University of Nebulon

• Think up a name. -Strength or Intelligence or Agility
  
• We should get those dead aliens out of his cabin. ASAP. -Success at it, I did Intelligence
  
• Where is your planet, young lady? -Tape (other is mask or nothing)
  
• Should we tell them the truth? -If a Strength/Agility name was chosen: No -If Intelligence one: -Yes
  
• I suggest blowing the bullies out of the sky, but I'm open to ideas. -I choose Strength (but seems any options here doesn't matter in the result)
  
• Fix the machine, Captain! -Intelligence or Strength, you must success at it!

Ending 2: You were wrong trusting the UFO

• Think up a name. -Strength or Intelligence or Agility
  
• We should get those dead aliens out of his cabin. ASAP. -Success at it, I did Intelligence
  
• Where is your planet, young lady? -Tape (other is mask or nothing)
  
• Should we tell them the truth? -If a Strength/Agility name was chosen: Yes -If Intelligence one: -No
  
• I suggest blowing the bullies out of the sky, but I'm open to ideas. -I choose Strength (but seems any options here doesn't matter in the result)
  
• Fix the machine, Captain! -You have to fail this so the one with more chance of failing

Ending 3: You were blown out of the sky

• Think up a name. -Strength or Intelligence or Agility
  
• We should get those dead aliens out of his cabin. ASAP. -Fail it (skeletons will be out even if failed, if the UFO is disappointed at you in the report, you did it right!)
  
• Where is your planet, young lady? -Nothing, so it will fail, again
  
• Captain, are you ok? -Battery
  
• We should find whoever gave them to him and give them the what for! What do you say, captain? -No
  
• Can you believe that? Raging data is out of control -Nothing

Ending 4: Our UFO and S.A.L.L.Y got married, 'til shutdown do they part

• Think up a name. -Intelligence
  
• We should get those dead aliens out of his cabin. ASAP. -Success at it, I did Intelligence
  
• Where is your planet, young lady? -Tape (Probably the Mask works too)
  
• Should we tell them the truth? -No
  
• Is there anything we can spare for him? -Gun or Handbook or Battery
  
• Will you encourage him to keep pursuing his passion? -No
  
• Should he take a second chance? -Yes

Ending 5: You joined up with your UFO and recorded a hit song.

• Think up a name. -Intelligence
  
• We should get those dead aliens out of his cabin. ASAP. -Success at it, I did Intelligence
  
• Where is your planet, young lady? -Tape (Probably the Mask works too)
  
• Should we tell them the truth? -No
  
• Is there anything we can spare for him? -Battery
  
• Will you encourage him to keep pursuing his passion? -Yes
  
• We need to do something, quickly, if he'll ever be taken seriously. -Lighter or Communicator

The Last Supper
Enjoy the last meal before the job.


Follow the Ending 1 from the Commissar Laika chain. Once all the dogs are on ship and the Heist is about to begin, an event about sharing Soup will appear, share it and the achievement is yours.