In the Soloman Wayne Courthouse (the courthouse in the beginning of the game when you rescue Catwoman, who is hanging over a pit of acid, from TwoFace), you can talk to the Calendar Man, who is locked up in the basement. You will notice a calendar on the wall next to his cell with 12 days circled.
If you talk to Calendar Man on each of these days, he will tell you a story about someone he murdered on that day. The corresponding month will also be crossed off the calendar.
To get this achievement quickly, disconnect your console from the internet, and change the consoles system date. Then speak to Calender Man, and then walk out the back door to get the game to save.