1: In the first part, Zed will be randomly jumping around trying to kill you while throwing letters at you.
2: In the second part you will need to destroy the speakers that Zed gets on top of. He will also throw balls at you but these are NOT the ones that you need to dodge for the achievement.
3: The third part is where you will get this achievement. Zed will be throwing these blue, and electric balls towards you. You will need to jump to avoid them, then dodge them by pressing O when they come back. Do this 15 times and the achievement is yours.
- Here's a tip to get him to throw the balls faster: if you leapfrog over him after one of his attacks, he'll usually go into the throwing ball attack immediately afterwards. Just keep leapfrogging him until you get the achievement.
You also can do this through multiple playthroughs, it does not need to be completed in one fight.