How to improve reputation?

Solution 1:

Still searching for a better way, but so far here is what I have:

What you do is you accept a patrol mission from a neutral/friendly base (such as in Distant Fume).

Patrol missions will always (as far as my experience goes) go though multiple zones, some of which have PMC stations. When that happens, any enemies destroyed grant reputation due to the fact that you are 'protecting their station'.

It works but it's very very slow.

Solution 2:

If the raider is not near Plutarch station, take a shot at it and fly close to Plutarch station. It will follow, then destroy it.