Heres the formula to the boss: He will charge attack you after taking a certain number of steps(~7), else he will just normally attack you. He does get faster as the level progresses, but not fast enough that it will take less than 7 steps to reach you. Headshots do the most damage.

A Parting Shot 2! + New Bosses! + More Enemies! + Improved Graphics! + Improved script! - No More Glitches! A Parthian Shot- A military tactic employed by the Parthians who would, while mounted, feign retreat; then, turn their bodies back to shoot at the pursuing enemy. Thus I present to you- A Parting Shot 2.