To earn this trophy, you need to kill 40 enemies with science weapons -- essentially the weapons involving fire and electricity. Some examples you'll find first are the Arc Cannon and M86 Thermite Rifle, which I'll be using for this guide. The M86 Thermite Rifle in particular can be used to complete an additional trophy at the same time!
There is no in game tracker for science weapon kills.
Instead, just go to the Main Menu, select Chapter, click right to Chapter 3 - "Inequalities", then scroll down to the "Enemy Contraband" checkpoint and load from here.
Sit through a few cutscenes, and you'll gain control equipped with an M86 Thermite Rifle. You can shoot a cloud of ignitable gas/powder with
to surround enemies. Then, press
to shoot a ball of fire that will erupt the cloud into flames, earning a science weapon and
incineration kill.
To reach your 40 science weapon kills, just kill every enemy in the area until the middle barn blows up, then pause and reset the checkpoint. Repeat that process until the trophy pops. It may take about 5-6 runs. (Restarting does not reset kill total, and you only have to watch the last 5 second cutscene after the first time).
Please vote if you found this helpful, and comment if you have any additional insight or questions. Feel free to add me on TT, TA, PSN, or XBL, username: Danokitty.
Happy hunting!
-Dan