Max Payne 3 Walkthrough played on Hardcore with free aim. I take no damage from enemies and don't use painkillers or assisted aiming. This means that if I take damage, I restart from the checkpoint. Hardcore allows enemies to kill you in 1-2 shots, so the best way to beat it is to take as little damage as possible, or, in my case, no damage.
There are, however, certain sections where damage is unavoidable (like the boat chase in Chapter 5). These sections are exempt from the rules, since it would be impossible to take no damage.
Act 2 (Coming Soon)
Act 3 (Coming Soon)