Here is the full list of all 57 IXION achievements.
The base game contains 56 achievements, and there is 1 DLC pack containing 1 achievements.
Finish the prologue
Discover Outer Hope during the prologue
Entertain your crew members
Destroy the Piranesi before it destroys a planet
Finish the game by following the path of genetic conatus
Finish the game by emancipating yourself from DOLOS
Finish Chapter 1
Finish Chapter 2
Finish Chapter 3
Finish Chapter 4
Adopt the borzoi
The borzoi survives the journey
Replace Edden with the P.A. of the Protagoras
Free ZY6073
Finish the chain of events concerning the strange spheres
Have a member of Tiqqun compose a rap song about the Administrator
Discover the ruins of the genetic facility
Unlock a sector
Unlock all sectors
Awaken a human from cryogenic sleep
Build all solar panels
Implement a new decree
Find two large resource deposits using a single probe
Build a memorial in each of the six sectors
Visit 15 planets
Have the Tiqqun's hull integrity erode below 5% and survive
Restore the crew's trust after reaching 1%
Reach 1000 population
Reach 3079 population
Experience a blackout for the tenth time
Build a Hull Temple
Convert waste into alloy, electronics or polymer
Train your first colonists
Use the body of Oulixes to access the Thiaki
Use exoskeletons to ensure no crew members die on Fargo 39
Fail to make it past the prologue
Have fires in 20 buildings at the same time
Reach tier 2 of the Industry specialization in a sector
Reach tier 2 of the Food specialization in a sector
Reach tier 2 of the Population specialization in a sector
Reach tier 2 of the Recycling specialization in a sector
Research every single upgrade for the Drone Bay
Destroy 200 buildings in a single playthrough
Skip a transmission within 1 second of it starting
Have an Observatory in each of the six sectors
Have a Train Station in each of the six sectors
Build an Exo-fighting Dome
Build a Health Center
Have 5 accidents within a single cycle
Transfer 300 resources between sectors in a single cycle
Have 5 Mining Ships active at the same time
Replace the last original piece of hull through EVA repairs
Have every single sector in a work status of at least "Overwork"
Reduce all audio sliders to 0 in the settings menu
Have a Water Treatment Center in a sector with the Body Recycling decree in effect
Implement the Naomi protocol 3 times
Complete Challenge mode