If my opponent used Iron Boulder ex's "Repulsor Axe" attack, will my Attacking Pokemon with Mist Energy attached receive the 8 damage counters from "Repulsor Axe" if I attack and do damage to Iron Boulder ex?
No, it will not receive the 8 damage counters. Mist Energy prevents all effects of your opponent's attacks done to the Pokemon where it is attached, and Repulsor Axe's damage counters are an effect of your opponent's attack.
Repulsor AxeMist Energy