Here is the full list of all 39 Ashes of the Singularity achievements.
Won a match by destroying all opposition
Won a skirmish game as the Post-Humans
Stomped the comp with human teammates
Won a skirmish with a handicap
Called in orbital support
Won a match on victory points
Didn't even sweat wasting 3,000 metal in a single match
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 Substrate
Won a skirmish against unfair teams
Win a match after a teammate has lost. Thanks a bunch, pal.
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 match without wasting a single resource
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
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 first Ascendency mission
Complete the second Ascendency mission
Completed the third Ascendency mission
Completed the fourth Ascendency mission
Completed the fifth Ascendency mission
Completed the sixth Ascendency mission
Conquered Artorius
Completed the eighth Ascendency mission
Completed the Tutorial
Conquered Roceda
Conquered Silgul
Conquered Falness