You only need to complete the last section of all four levels of the Story mode on the Nightmare difficulty level. Nightmare difficulty is noticeably a step up from Normal, and even with 4 players over Live, some parts can be extremely tricky. You can load up the last section of each level on Normal or Nightmare after previously completing it on any difficulty. This works in Co-op as well, but the host must have the last section unlocked.
Note: You can use this trick to unlock all the complete level related achievements as well as the Co-ordinated Fire achievement.