Here is the full list of all 39 Ashes of the Singularity achievements.
Fielded 1,000 Logistics worth of units
Conquered Artorius
Conquered Falness
Completed the sixth Ascendency mission
Reached level 10 in any global upgrade
Won a match by destroying all opposition
Completed the fifth Ascendency mission
Conquered Roceda
Won a match on victory points
Completed the fourth Ascendency mission
Called in orbital support
Completed the third Ascendency mission
Didn't even sweat wasting 3,000 metal in a single match
Complete the second Ascendency mission
Completed the first Ascendency mission
Won a match without wasting a single resource
Lost a skirmish game
Won a six-player match in the Ascendancy Wars
Won the Ascendancy Wars for the Post-Humans
Won a skirmish game as the Post-Humans
Won a skirmish game as the Substrate
Won a skirmish against unfair teams
Win a match after a teammate has lost. Thanks a bunch, pal.
Stomped the comp with human teammates
Joined a ranked match
Stuck around to the bitter end in a multiplayer loss
Reached rank 5 in ranked multiplayer
Reached Legendary status in multiplayer. #respect
Won a 3+ player free-for-all game as Substrate
Won a game after your Nexus was dealt critical damage
Reached level 5 with a Dreadnought
Fielded 30 units of bombers at once
Won a skirmish with a handicap
Defeated an unfair-teams skirmish against Insane AIs with a fellow human fighting at your side
Defeated an unfair-teams skirmish against Insane AIs with no human help
Completed the eighth Ascendency mission
Completed the Tutorial
Conquered Silgul