You can start earning this achievement when you first step out onto the beach. Use RB to select the fists on the bottom of the weapon wheel. Nothing can be equipped in order to make progress for this achievement "brass knuckles will not work either."
- I find it easier to kick zombies LB to the ground and punch them until they die.
- Separate your zombies, attack them one at a time so you do not get swarmed.
- Keep an eye on your stamina, you will lose a lot punching zombies.
After your 25th kill your achievement will unlock.