To obtain this achievement you need to unequip all your melee weapons.
Then it's simply a matter of killing 500 enemies with the robots bare hands. I would suggest the small aliens that attack you in huge swarms. They die very quickly.
Note that Mr Riggs' bare hands look exactly like the power fists. So it's very easy to mix those up.
That's why would suggest to unequip all of your melee weapons, just to be super duper safe.
You'll know you're doing it right when Steam will update the achievement progress.
It shouldn't take long to get required amount of kills.