This trophy is a lot more simple than it sounds in the description.
I'm unsure of the many possible ways to achieve this, but
all I had to do was simply punch my enemies to death, yup.. You may want to be cautious depending on your difficulty but I was playing on Normal, and if I got shot up too much punching my enemies, I'd just activate my armor mode with
.
To punch your enemies, just simply click in the right analog stick until they die, CELL soldiers take 2-3 hits, CEPH stalkers take a good 10+ maybe, I achieved this before the end of the second mission, "Welcome to the Jungle"