Dying Light Mouths Wide Open Trophy / Achievement will give you one Silver trophy or 25 gamerscore points. To get this Trophy / Achievement you must kill a Volatile.
Volatiles only spawn at night, if you are in a day just go to bed to start the time of night. Volatiles have a huge health of 3000, are very fast and last but not the least cause massive damage. Keep an eye on the mini map from their presence.
If you are noticed by any of the Volatiles it will surly hunt you and they tend to spawn quickly in the tower area which is the zone in the Slums where game starts and where most main missions begin.
The most easiest and reliable way of destroying a Volatile is luring it to the electric fence traps around the tower. Let the Volatile notice and then chase you. When it gets into the trap it will die, if that does not happen, your second chance is another trap located on the other side of the building.
These traps are self recharging and are ready again after about 30 seconds. For extra precautions use grenades or firearms to fully destroy the Volatile.
If you are still not sure, watch the following video on how to get the Dying Light Mouths Wide Open Trophy / Achievement. This game is now available on PC, PS4 and Xbox One.