There should be some story progression achievements, of course (one each time you unlock a new planet/station excluding seasonal ones, and one for each side-quest with more for those with multiple important decisions; possibly one each time you recruit a new crew member?). In addition to those, I've some more ideas:
You Don't Have To Put Everything You Find In Your Mouth: complete the game without using any transformatives.
Walking Disaster Zone: get both Tarkus and Myrellion blown up in the same playthrough.
Cat Fight: as a kaithrit or half-kaithrit, defeat either Kara or Shade in combat while having the other as an ally.
Broodmother: raise your Fertility and Fertility Speed Modifier to at least 1000% each, then give birth to at least 50 children in one in-game month.
Clown Car: without using any cheat codes, recruit more crew members that take up crew space than your ship has module/crew capacity and fly to another location.
Corrupted: reach 100 Taint.
Pure: complete the game without going over 10 Taint.
Treating You Right: across all playthroughs, experience every variant of the Treatment.
Heavily Modded: mod yourself away from your original race and equip two cybernetic implants.
We're Both Gonna Be The Mommy: be pregnant with an NPC's children at the same time as they're pregnant with yours*.
Fortunately, I Like Crowds: have a threesome, foursome or moresome.
Audience Participation Encouraged: become an Ultra-Exhibitionist and have sex in public.
Friends In Low Places: befriend Kiro Tamahime, Kara Volke, the Rat's Raiders and Amara Faell.
Going Native: formally establish positive relations with at least three pre-industrial societies^ in one playthrough.
Addiction Addict: reach at least 50% addiction to at least four people or substances**.
Pirate Lord: earn the respect of all five of Zheng Shi's gangs.
'Tis A Silly Place: activate Silly Mode.
Pacifism Run: complete the game without completing any unnecessary combat encounters^^ (fleeing combat is fine).
More Of A Dog Person: starting as a half-ausar and remaining a canid race, have sex with most of the more canid non-hostile NPCs***.
More Of A Cat Person: starting as a half-kaithrit and remaining a felid race, have sex with most of the more felid non-hostile NPCs^^^.
Obviously, the 'complete the game' achievements won't be possible until the game's main story is actually finished.
*e.g. Ilaria, Mirrin, the Frostwyrm, any of the Bored Jumpers.
^e.g. befriend Quinn and her tribe, marry/subjugate Taivra, successfully complete the Siege of Korg'ii Hold.
**e.g. red myr venom, bothrioc oil, Ardia, Luca, Lumi, Lane.
^^so far, this means only beating Tam, either Khorgan or the Nyrean Praetorians, Urbolg, Feruze and the Shock Hopper.
***canid races include ausar, huskar, korgonne and their half-breeds`, dog-, wolf- and jackal-boys/girls/morphs.
^^^felid races include kaithrit, naleen, milodan and their half-breeds`, cat-, lion-, etc. boys/girls/morphs.
`regardless of what their other half is; as such, Saendra, Astra and Ziresh count towards both of these.
