You can actually do both reputation trophies in one playthrough as factions can both love and fear you at the sane time.
For my trophy I annoyed the board by siding with Phineas everytime, also killing any corporate I see.
Destroyed MSI and then killed any survivors I found.
Then Killed all sublight employees on Groundbreaker, traveled to Monarch and killed them in their outpost until the trophy unlocked.
Iconoclasts are also easy to use to boost this trophy.