As of writing, you need to have played enough to have moved off of the lowest rank for at least one of the trading, exploring or combat ranks. For example, move from Harmless to Mostly Harmless in the combat rank.
See here for a rank overview: http://elite-dangerous.wikia.com/wiki/Pilots_Federation
Once you have moved up at least one rank in any discipline you will be able to go to the Navigation console screen (hold
) and then use the dpad to select Galactic Powers (final option on the left).
This will bring up a screen split into three options. On the second option, when selected, you can see all of the powers and an overview of their faction, rewards and territory. There is also an option here to pledge allegiance at the very bottom of the screen. Select that and the achievement will pop.
Once aligned with a power the previously blank third option for selection will populate with a portrait of your aligned power and from there you can view more information about missions and ranking - although to get this achievement all you need to do is pledge, nothing more.