This trophy is entirely community orientated.
The whole game acts as an ongoing fight for territory, every planet you win against a race you'll gain Community Influence which will help push the yellow progress bar, if the community fails somewhere (this does happen fairly regularly) and the red bar fills up before the yellow one you'll be prompted to defend a capital city to regain control.
Capital defenses have a time limit of 2 hours in which you'll have the option to play missions of varying difficulty against that race to fill up another yellow bar. The community will need to make a push together as the defence has to be successful within 2 hours.
Similar to homeworld assaults you'll be able to pick a level 3, 6, 9 or 12 mission.