In order to unlock New Game+ and it's many variations, you have to be the game at least once. This can be done on any difficulty. If you want a little bit of variety in your second playthrough you can choose from the following NG+ Variants:
Playing Classic NG+ changes the look and feel of the game slightly to call back to the original Dead Space game. Difficulty increased and in-world aiming is turned on. Necromorphs do increased damage.
This mode unlocks the Devil Horns.
Pure Survival turns your NG+ into an episode of one of those survival shows on the Discovery channel. You will find no health, ammo, or stasis packs in the world, only raw resources. If you want a health pack, you better dig for the material to craft one.
This mode unlocks the MK-II Overclocked Parts Set and Mega Resources Deposit.
This is the hardest difficulty mode in Dead Space 3. It's Impossible Difficulty and you cannot die. Not once. Because of Dead Space 3's auto-save, they've done anyway with any save limitations and just said flat out that you'll be sent back to the beginning if you die.
This mode unlocks Retro Mode