If you encounter the Sol system have a science vessel survey the system. Sol III is earth. Special text for discovering a sentient species will appear stating the planet is at war. I don't know if it does it 100% of the time but both times I've found the planet it has said that and had an Iron Cross next to the Sol III name. Build troop transports and invade the planet. 4 armies will do the job. You must successfully conquer the planet for the achievement to unlock. I can speak from personal experience a failed invasion will not unlock the achievement.