To unlock this achievement you must finish the level by killing any enemy you engage in battle with before the timer in the top left runs out. If it does run out a bell card will appear and you will have to load up your last checkpoint.
I came back to this mission after I was nearly at the end of the game. I found when trying to complete this mission with lower level characters they were unable to kill the three enemies down by the shore fast enough.
I would suggest using the frog hex card and stepping on one of them as a quick way to eliminate an enemy.