The Max Payne 3 Story can be played at five difficulty settings that can be adjusted on the fly and provide varying levels of challenge as follows:
Easy: Increased Health and Bullet Time® Rewards. A satisfying challenge
Medium: Moderate Health and Bullet Time Rewards. A stiff challenge
Hard: Low Health and Bullet Time Rewards. A real test
Hardcore: Minimal Health and Bullet Time rewards. Very challenging
Old School: Last Man Standing is disabled.
Medium is the default setting for all - so you can start the game and decide from there on the fly whether you'd like to adjust your difficulty for more of a challenge or an easier go as you play.
Easy and Medium settings feature dynamic difficulty which provides access to extra painkillers to help you pass particular parts of the game if you've died repeatedly. On Easy and Medium settings, when you die at a checkpoint, you restart the checkpoint with at least one full magazine of ammo in each gun (except grenade launchers) and the number of painkillers that you started with. For every three times you die at a checkpoint, you get one extra painkiller. So if you started a checkpoint with 2 painkillers, and died 3 times, on each subsequent retry of that checkpoint, you'd start with 3 painkillers. If you died 3 more times (6 total), you'd start with 4 painkillers on each subsequent restart. On Easy and Medium, this can continue until you are respawning with a full 9 painkillers.
On the Hard setting, there is also dynamic difficulty however it is intentionally much more limited to ensure a tougher go. On Hard, if you die 5 times, you will get a bonus painkiller on subsequent respawns, and if you've died 10 times, you can get one more. However, it will never give you bonus painkillers that make your total go above 2. So if you started a checkpoint with 1 painkiller and died 5 times, you'd start with 2; but if you died 5 more times (10 total), you would not get an extra - you would continue to respawn with 2. Likewise, if you start a checkpoint with 3 painkillers, you would never get a bonus painkiller in Hard mode.
Hardcore and Old School modes are unlocked by beating the Story on Hard difficulty.