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.
Use exoskeletons to ensure no crew members die on Fargo 39
Convert waste into alloy, electronics or polymer
Implement a new decree
Discover Outer Hope during the prologue
Finish Chapter 1
Use the body of Oulixes to access the Thiaki
Awaken a human from cryogenic sleep
Unlock a sector
Finish 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 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 all sectors
Build all solar panels
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
Train your first colonists
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