Complete the Tutorial
Say yes to the tutorial when creating a new save.

Collect a Bunny stuffed-animal
I found the off-whitish stuffed bunny in a Hazard Level 3 Mackerel Exolab very early in the game. Just go up to it and pick it up. It was really hard to miss in my case.

Complete Act I of the campaign.
Reach level 7, I think.

Complete all Salvage Goals on a Atlas Class Ship.
First Atlas class ship unlocks at rank 5. The only thing to really keep in mind is that you have to cut 4 fuel pipes in each engine, pull the engine out, then fly to the end of the engine housing to cut the fuel before the burning fuel pipes reach the tanks at the end. Naturally, cutter upgrades (especially heat capacity), grapple upgrades (especially strength), and thruster upgrades (especially velocity) really help here. Reach the fifth tier for salvage on an Atlas and the achievement should pop.

Complete all Salvager Goals on a Javelin Class Ship.
Javelin unlocks at rank 7. The early Javelins are pretty self explanatory. Only two things are really worth mentioning: 1) The front and rear portions are often separate in terms of pressurization so make sure to depressurize both sections. 2) Clamped on cargo on the exterior can be removed by cutting the interior of the clamp and then sliding the cargo off away from the ship.

Unlock Demo Charges
The demo charges become available for purchase at rank 11. It must be purchased for 120 Lynx Tokens to pop the achievement.

Complete all Salvage Goals on a Gecko Class Ship.
The first Gecko unlocks at rank 14. Because of the size of them and the general lack of airlocks, it is pretty much impossible to not violently decompress them. Make sure to to grab on before opening doors and stay out of the line fire for debris flying through decompressing hatches. I also recommend completely stripping the exterior before tackling the reactor. When you're getting ready to deal with the reactor, first remove all of the panels enclosing it carefully and the plate on the top so it's exposed. If it's exposed, should have plenty of time to grab the coolant canisters, fly out of the ship, pluck the reactor out of the housing, and push it into the barge.

Complete Act II of the campaign.
Reach rank 17 and start a new day. A cutscene will play and when it concludes, the achievement should pop.

Finding the Hidden Data Drive.
It's taped to the back of the HAB. If you're having difficulty finding it, you can buy the scanner "object" upgrade and use that to find it easily.

Complete Act III of the campaign.
Complete "Industrial Action," pay off debt, finish Beulah, and terminate your contract. It'll pop during/after the cutscene.