When the Core Design copyright screen appears, quickly press Up, Down, Left, Right, Down, Down, Right, Right, Square. A debug menu will appear.
Start a game then quit by pressing Start+Select. Now at the Main Title Screen, press Up, Up, Up, Down, Down, Down, Right, Right, Triangle. You'll hear a sound to confirm correct entry.
At the Briefing screen, open the locker and enter the code 4L2CZCQKDAABACQDB. You'll begin the extra mission.
Thanks to Revolution readers Daniel Fortea and Nate Barnes!