Empire of Sin

This can be done at any time, but I’m pretty sure you will have had to have completed or skipped the tutorial first. Personally I would suggest you save before attempting as your bribes won’t always be successful and/or you can reload after the achievement pops so you don’t actually spend the money.

So from the radial wheel you can open up the Diplomacy screen. Cycle through the different Mob Bosses and smaller gangs until the Police are selected. On the second tab, there will be a list of options for interacting with your selected faction. With the Police selected, the top option will be “Bribe to improve relations”. Select this and choose the amount you want to bribe them with. I would just go with all your available money - so long as you plan to reload your save afterwards. You will then get a message telling you if you were successful or not and hopefully an achievement. If your bribe failed, reload and try again. It should only take a couple of tries unless you’re super unlucky.

I got super lucky with this one. I just happened to save a few moments before the dialog box popped up saying they are going to raid one of my rackets, you could see the BOI markers on the world map before it happens. It cost me nearly $9000 for the bribe, which has a %50 chance. Took me three reloads of the previous save and the bribe chance happened every time.

So once you see the symbols on the map, kind of a blue police light with three lines coming out the light blub, just save and wait to see what happens.

If the police are casing a racket, don't close it, they will eventually send the BOI to investigate..

It's very random so good luck.