The Empire is the second of the superpower factions that allows you to move up within its ranks though at the moment no achievements are specifically tied to this faction. The ranks and rewards for moving up are as follows: This faction is required to gain access to Sol and with it an achievement so moving up within their ranks must be done at some point. The Federation is the oldest of the three factions originating from humanity's home system of Sol. With that done lets move on to the main two factions. There are a great deal of resources all over should this style of play interest you. If you wish to learn more about the Powerplay system you can check out this excellent and detailed guide on the subject - Powerplay Guide.
The Powerplay system is very in depth and other than the above achievement no more interaction with it is need at this time.