Here is the full list of all 18 Achron achievements.
Beat Campaign 1
Beat Campaign 2
Beat Campaign 3
Beat Campaign 4
Beat C1L4 with Holloway catching Tyr lying to him
Beat C1L7 without making any gates or carriers
Beat C1L8 without making any aerospace units
Beat C2L5 while meeting up with the stranded Vecgir
Beat C2L7 in under 30 minutes
Beat C3L4 without using any chronoenergy
Beat C3L5 avoiding any waves of air reinforcements
Beat C3L7 or C3L8 with the Octoligo guards all dead
Beat C4L1 without building anything at all
Beat C4L3 without allowing the operators to escape at all, achronally
Beat C4L4 with no resources remaining in any crates
Beat C4L7 killing every single enemy on the level
Beat the Sandbox Chronoclone Challenge in a minute or less