Here is the full list of all 39 Ashes of the Singularity achievements.
Conquered Artorius
Conquered Falness
Completed the sixth Ascendency mission
Won a match by destroying all opposition
Completed the fifth Ascendency mission
Conquered Roceda
Lost a skirmish game
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
Fielded 1,000 Logistics worth of units
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
Reached level 10 in any global upgrade
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