To unlock the New Game + mode in The Darkness II, simply complete the game on any difficulty. This allows you to play through the game for a second time, or any time after that, with your character intact from the previous play. You can use this mode to get the remaining relics that you couldn't get on your first playthrough.
Check out our exclusive guide http://www.supercheats.com/guides/the-darkness-2 for this sequel that puts players back in control of Jackie Estacado, the wielder of The Darkness. There are currently no known push button cheats for this game but our guide will more than help you navigate through the game. The guide includes finding ALL the relics and an Achievement guide.