Take a look in the spoliers forum, there is a list with all the bribes and their locations listed.

killing a few of a factions enemies always helps

Get the best fighter you have and go on a rampage against their enemies in the weakest system they have some in. It's amusing to beat down waves of horribly weaker fighters, and pretty soon you'll have a good enough reputation to land on their base. There's almost always a fixer on their own base.

Also, sometimes the fixer fixes for multiple factions. You have to visit him more than once sometimes to be able to do the right bribe.

*light spoiler

kill bounty hunters
if you using light fighter seach them at the system that you landing after disaster..
and advance to other system if you had more advance fighter..
using this method your reputation with many pirate will increase, not only with certain pirate if using dollar sign..

You don't need to beat on bounty hunters to get in good with the big bad pirate factions. Heck, you don't even need to make any new enemies.

The first step is in Manhattan, where you park yourself mid-trade lane and start blasting transports. Make sure no single faction goes below midlevel neutral, but keep killing transports in general. The Lane Hackers should be the first to lose their hostile status.

Then you go to Freeport 6 in Tau-29, where you can bribe the Outcasts with all that cash made off of blasting transports. This pushes the Hacker rep up more, too.

After that, head to Freeport 9 in Omicron Theta, where you can bribe the Corsairs. This will push the Outcasts neutral again, but nothing will go hostile if you play your cards right.

Now go to Bruchsal base, in the Frankfurt system. Bribe the Red Hessians. THis will push the Corsair rep neutral, but should leave the Outcast and Hacker ratings alone.

Through all that, the bounty hunters don't go hostile. There shouldn't be any hostile corporations or houses, either. Now you have pretty much free range through the Omicrons, Taus, Sigmas, and Omegas.

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Reaper: $200,000,000.
Rockets: $100,000
The look on that pilot's face when you launch a full pod of screamers up his tailpipe: priceless
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You're not just beating the dead horse, you're cutting down trees to do it with!