While the trophy description seems extremely straightforward, I think there is more to it than it sounds. The description is simply:
Killed 10 Machines weak to Fire while burning, or weak to Freeze while frozen.
However, I've taken out 6-7 Corrupted Zones by setting all Machines within them on fire and made sure to let them die while burning. At this point, I'd estimate that I've killed at least 20-30 Machines weak to Fire while they were burning, yet this trophy hasn't popped. Do I need to kill them with non-elemental damage while they're burning/frozen to get the trophy or something?