Okay, so I have been making sure to pick up and complete side-quests as often as possible (9 hours in ish) and this Achievement popped for me with the following Reputation:
Groundbreaker - Revering - 87% Positive, 1% Negative
Iconoclasts - Neutral - 0% Positive, 0% Negative
Monarch Stellar Industries - Neutral - 0% Positive, 0% Negative
SubLight Salvage & Shipping - Neutral - 0% Positive, 0% Negative
The Board - Neutral - 9% Positive, 0% Negative
Deserters - Revering - 100% Positive, 0% Negative
Spacer's Choice - Nervous - 96% Positive, 100% Negative
I'm not sure if this is a bug or what. I tried to remain on the good side of everybody (but diverted Geothermal Plant power to the Botanical Lab, depriving Edgewater of power).
I know it's not a perfect guide but it seems to be simple enough, just keep questing I guess, lol.