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 game by following the path of genetic conatus
Destroy the Piranesi before it destroys a planet
The borzoi survives the journey
Finish the game by emancipating yourself from DOLOS
Finish Chapter 4
Implement the Naomi protocol 3 times
Finish Chapter 3
Reach tier 2 of the Food specialization in a sector
Have a Train Station in each of the six sectors
Unlock all sectors
Build all solar panels
Build an Exo-fighting Dome
Reach 3079 population
Build a Health Center
Visit 15 planets
Adopt the borzoi
Finish Chapter 2
Convert waste into alloy, electronics or polymer
Destroy 200 buildings in a single playthrough
Skip a transmission within 1 second of it starting
Replace the last original piece of hull through EVA repairs
Train your first colonists
Implement a new decree
Reach 1000 population
Use exoskeletons to ensure no crew members die on Fargo 39
Entertain your crew members
Finish Chapter 1
Use the body of Oulixes to access the Thiaki
Unlock a sector
Find two large resource deposits using a single probe
Awaken a human from cryogenic sleep
Finish the prologue
Discover Outer Hope during the prologue
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
Build a memorial in each of the six sectors
Have the Tiqqun's hull integrity erode below 5% and survive
Restore the crew's trust after reaching 1%
Experience a blackout for the tenth time
Build a Hull Temple
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 Population specialization in a sector
Reach tier 2 of the Recycling specialization in a sector
Research every single upgrade for the Drone Bay
Have an Observatory in each of the six sectors
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
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
Complete Challenge mode