So im in Eurybia and trying to gain access to my power plant upgrade.
I need to be an outsider..
What would be the best way to go about this?
I have a..
A rated Vulture
A rated type 6
A rated Asp Explorer
A rated Cobra MkIII
Go do some missions for a minor faction that is associated with the empire. Eventually you should see a mission that will allow you to rank up in the imperial navy reserve. Once you get to 100% toward the next rank. I think outsider is the first or second rank for the empire. Shouldn't take long. Your Asp X is probably your best bet, as it can do anything.
Be aware that the Imperial Navy missions won't necessarily spawn as soon as you reach 100% in your current rank.
But don't worry, additional work for the superpower won't be lost, as further rank gains are still counted under the hood.
I also think (please someone correct me if I am wrong) that you'll need at least a 'friendly' status (and maybe even 'allied') with a faction in order to get a Navy rank-up mission. And even if being allied isn't mandatory, it should help the probability for the mission.
As rank-up missions can be created by any Imperium-allied faction, a station with many of them is beneficial.
Finally, there seems to be a bug currently, that prevents the Naval mission to spawn. (Personally I never ran into it, so I just report what I've read elsewhere). Anyway, if allied factions in your station of trust insist in their habit not to spawn those missions, try to relocate and look for it in another star system.
I believe the rank up missions are pure RNG. If you don't see one just keep looking at other stations with imperial factions. Also if you don't like the type of mission (e.g. assassination) just ignore it and look for a different one, there are all kinds of them including simple courier missions.
Find an Empire system with several large stations (this is surprisingly difficult because many Empire systems are small backwaters with outposts only). Run missions in AspX to build up rep until you get promoted.
So here I am in a part of Aisling Duvals space, about 200Lys from sol, and every single system is massive with multiple Orbis Stations and at least 4 empire loyal factions in it. Try the Velnambang/Tehuenef/Adachit/Di Yomi sphere. Also, i'm doing this in Mobius with a Type-6 set up for trading.