I Am The Night Mode will unlock after you have completed your New Game+ playthrough. Almost everything detailed in the New Game+ achievement applies to IATN Mode, which includes the removal of the counter indicator in combat and an upgrade in all enemy types.
The catch of this new mode however, is that you can not die AT ALL during this playthrough, for you will only have one life. If you are unfortunate enough to die at any time during the game, you will be reverted back to the Main Menu. The game will still have autosaved enabled, so don't worry about having to complete this playthrough in a single sitting. This is a nice reminder to fall back on when you are approaching a difficult section of the game and want to quit out of the Story or shut your console off.
A great tip to utilize during this playthrough - although a bit complicated - would be to grab a USB device and plug it into one of the ports of your Xbox. Now, when you reach a certain checkpoint or part of the game where you think you may die due to an upcoming boss battle or enemy encounter, you can quit to the Main Menu and then go to the Xbox dashboard. Now head over to the dashboard's System Settings and into your Memory hub. Copy your autosave file which is the "Hard File" onto your USB device. This acts a failsafe in case you die next time you boot up the game and try progressing through the story. Now head back into the game, and if you do end up dying at any point, simply go to the dashboard and reboot the game. At the Main Menu, when it asks you to select a storage device, choose your USB and you will resume the game at your copied autosave file.
This method might sound a bit complicated, and it's not entirely necessary either. An alternate, and much simpler method, would be to pause your game right before you're about to die or if Batman is in the slow motion death animation (before the black screen appears) and just quit out to the Main Menu. When you boot the game back up, you will continue from your last autosave.
Whichever way you decide to tackle this playthrough, just remember to be alert and quit out of the game IMMEDIATELY if you think you're about to die. Good luck, folks!