You'll encounter demolition mechs in chapters 2, 3 and 10, but chapter 3 is probably the easiest for this trophy.
Right at the end of chapter 3, at the point you gain stun ammo for the first time, you are in an open area with a few low walls. The demolition mech will smash though a brick wall and confront you. Quickly grab the plasma ammo in the corner and run through the hole the mech has just smashed; there is more plasma ammo to your left.
Stun the mech with the newly acquired stun ammo and change to plasma ammo. Aim for the mech's head, the reticule will turn red when it's a good shot, and fire every plasma round you have.
Once you have run out of plasma, it seems you may have to let yourself be killed. I tried reloading the checkpoint and the trophy did not unlock, even though I had made more than 20 headshots. But after dying and doing it over again a couple of times the trophy popped.
Maybe it was just slow to unlock, but to be on the safe side... let yourself die once you are out of ammo.