For this achievement you need reach 100 reputation with the mob.
Each day you'll usually find at least one activity that you can do for either the mafia, or the crew. Completing jobs and accepting deals from the mob will increase your reputation.
When you reach 100, go to the pizza restaurant and they'll make you an offer you can't refuse. Well, you can refuse, but don't and you'll earn this achievement.
It also takes you to a game over screen, so select the rewind time option from the menu and replay the day to continue the story.