In the game there is traps and environment hazards. For this trophy the enemies must die in these traps, not just be damaged. A few examples of traps/hazards would be the swining logs, exploding barrels, and acid puddles. There are many more. Act 1 Level 5 Boss, Mossback, kills enemies as he is doing his attacks and counts towards this.
This doesn't have to be done with one character. The kills are cumlative and counts with all characters and playthroughs.
DLC: If you have the DLC 'Jungle Hunt', this is made easier. The river raft ride where you knock enemies into the water counts towards this and makes this much easier to obtain. Happy Gaming!