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.
Destroy the Piranesi before it destroys a planet
Finish the game by emancipating yourself from DOLOS
The borzoi survives the journey
Replace Edden with the P.A. of the Protagoras
Finish Chapter 4
Build a Hull Temple
Have a Train Station in each of the six sectors
Unlock all sectors
Visit 15 planets
Have a member of Tiqqun compose a rap song about the Administrator
Build all solar panels
Build an Exo-fighting Dome
Entertain your crew members
Finish Chapter 3
Reduce all audio sliders to 0 in the settings menu
Reach 3079 population
Free ZY6073
Convert waste into alloy, electronics or polymer
Destroy 200 buildings in a single playthrough
Build a Health Center
Adopt the borzoi
Finish Chapter 2
Skip a transmission within 1 second of it starting
Experience a blackout for the tenth time
Replace the last original piece of hull through EVA repairs
Reach 1000 population
Have 5 accidents within a single cycle
Train your first colonists
Implement a new decree
Use exoskeletons to ensure no crew members die on Fargo 39
Finish Chapter 1
Use the body of Oulixes to access the Thiaki
Find two large resource deposits using a single probe
Unlock a sector
Awaken a human from cryogenic sleep
Finish the prologue
Finish the game by following the path of genetic conatus
Finish the chain of events concerning the strange spheres
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%
Discover Outer Hope during the prologue
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
Have an Observatory in each of the six sectors
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"
Have a Water Treatment Center in a sector with the Body Recycling decree in effect
Implement the Naomi protocol 3 times
Complete Challenge mode