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, you'll need the yellow bar to fill up in order to progress regions. Once the community has fought their way past the last region you'll initiate an attack on that races homeworld.
Homeworld attacks have a time limit of 48 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 assault has to be successful within 48 hours.
Similar to capital defends you'll be able to pick a level 3, 6, 9 or 12 mission.
Once you're successful that race will be eliminated for the duration of that war and you'll no longer be able to play missions against them.