Here is the full list of all 39 Ashes of the Singularity achievements.
Won a skirmish against unfair teams
Defeated an unfair-teams skirmish against Insane AIs with no human help
Won a skirmish game as the Substrate
Reached level 5 with a Dreadnought
Won the Ascendancy Wars for the Post-Humans
Completed the eighth Ascendency mission
Won a six-player match in the Ascendancy Wars
Conquered Falness
Conquered Silgul
Completed the sixth Ascendency mission
Conquered Artorius
Won a match by destroying all opposition
Didn't even sweat wasting 3,000 metal in a single match
Completed the fifth Ascendency mission
Called in orbital support
Conquered Roceda
Fielded 1,000 Logistics worth of units
Won a match on victory points
Completed the fourth Ascendency mission
Completed the third Ascendency mission
Complete the second Ascendency mission
Reached level 10 in any global upgrade
Won a match without wasting a single resource
Completed the first Ascendency mission
Won a skirmish game as the Post-Humans
Win a match after a teammate has lost. Thanks a bunch, pal.
Stomped the comp with human teammates
Lost a skirmish game
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
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
Completed the Tutorial