Beating the game on normal will unlock the extreme challenges for the Spirit Blade and beating the game on Joe must Die will unlock the extreme challenges for the infinite ammo. You must do either first. Challenges are not available in your first playthrough.
I recommend completing the very first challenge on normal mode with your fists in the first area. 3 molded to kill then smash the door and enter the shack where the cure is under 1 minute. You can kill the second and third enemy stealthy. You can also use the shotgun which is the fastest way. Nothing else. Really easy achievement.