Here is the full list of all 21 Planets Under Attack trophies - there are 21 bronze.
Successfully defend a planet with just a few citizens on it (except for offline multiplayer).
Complete 30 online multiplayer matches.
Capture a planet when you have no planets left in any mode except for offline multiplayer.
Win in each basic game mode: Elimination, Capture, Domination, King of the Hill.
Win an online team multiplayer match.
Earn all stars in a single mission in the Humanity Inc.campaign.
Complete all missions in the Humanity Inc. campaign.
Reach level 20 for Human race.
Reach level 10 for Robot race.
Win a 4 player free for all match against 3 hard AI.
Destroy one million enemy population. Yes, 1 000 000.
Complete half of the Humanity Inc.campaign.
Get 5 stars in the Humanity Inc.campaign.
Get 10 stars in the Humanity Inc.campaign.
Get 20 stars in the Humanity Inc.campaign.
Get 30 stars in the Humanity Inc.campaign.
Get 40 stars in the Humanity Inc.campaign.
Get 50 stars in the Humanity Inc.campaign.
Get 60 stars in the Humanity Inc.campaign.
Purge all Swarm planets before completing the mission.
Trick Destrobos' death planet into attacking its own ally during the boss battle.