@Eternal_Montage posted the most efficient way to raise Faction standings. ‘The Plan’ can be customized to fit each players own specific situation. With proper planning and due diligence, the various steps outlined in it can be completed quickly and easily.
First things first, if you want to keep from getting negative standing hits, decline all combat missions against Empire Factions, only accept combat missions against Pirate Factions.
Storyline mission offers can be declined or ignored with no penalty incurred. Now if you want to do those mission offers, then it’s best to do ‘round-about’ mission runs (16 + Storyline) with each of the various Empire Factions to help keep their standings more equal.
Definitely train up Social, Connections and Diplomacy skills. Also might as well train up Negotiation and Fast Talk too. And if you’re interested in obtaining items from Loyalty Points Stores, then train up the LP skills associated with each Agent Division.
Social will increase amount of standing gained for completing missions.
Connections will increase your current positive standings.
Diplomacy will raise your current negative standings.
Negotiation will increase amount of mission reward payments.
Fast Talk will raise amount of security status gained for destroying Bounty NPC’s.
Security, Distribution and Mining Connections will increase amount of Loyalty Points gained for completing missions associated with those Agent Divisions.
By working ‘The Plan’, I currently have positive standings with 13 Empire Factions, the 4 main Empire Factions are just shy of being +8.00 standing and only the Pirate Factions are negative.