It's best to run as the Engineer class for this, as you will gain money back from using traps. By the time you reach the end of the City section you should gain this Trophy, as the final Hive is near multiple Fire and Electric traps right near it, and many many enemies will come towards that area.
Also in the final section, traps are a bit more scarce as well as the enemies are much stronger, so getting trap kills in the last area is much tougher. This, like the Scavenger trophy is best done with only one person in the group attempting it in a run, but as long as you arm traps as soon as the drill starts, you shouldn't have much trouble with this.