While this can be achieved by conquering or assimilating another Empire's homeworld, it is perhaps most easily achieved by conquering the homeworld of a primitive pre-FTL species.
1) Identify a primitive species close in proximity (or within) your Empire's borders, and claim it. If this planet is outside of your borders, first construct a frontier outpost within the system.
2) Build a number of 'Assault' soldiers from your home planet. When this has completed, 'Embark' them and send them to the primitive species' planet.
3) Commence assaulting the planet. With six or more armies you shouldn't have too much trouble -- however if the species is in the Industrial or Post-Atomic age, you might encounter stronger resistance, requiring the designation of a General or reinforcements.
4) Once the planet has been conquered, the achievement will pop.
NOTE: In order to conquest a primitive species, your Native Interference policy must be unrestricted. Certain traits, such as xenophilia, will prevent you from earning this achievement for as long as your Empire has them.