Here is the full list of all 19 Planetary Annihilation achievements.
Smash five enemy planets
Win against three times as many players
Destroy five enemy planets with annihilasers
Activate an annihilaser
Eliminate a faction in galactic war
Build every kind of basic factory
Start a game with a custom system
Use more than 95% of the metal and energy you produce in a match
Annihilate your opposition throughout the galaxy
Participate in ten team games
Target an incoming planet with an annihilaser
Discover a new loadout in galactic war
Watch competitive play for two hours as a spectator
Watch competitive play for eight hours as a spectator
Kill a commander within five minutes, five times
Manage your armies with all ten control groups
Keep tabs on your conquest with ten camera anchors
Build every structure in a single game
Build every kind of unit