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