Easiest way to get this achievement is to just use melee and grenades to kill all the enemies. Highly recommend you do this on easy to save you stress. Using cannons or gatlings and missing will likely cause you to not get the achievement. You have to make at least 1 shot (or else you will be at 0%) and make sure it hits. If it does continue using melee. If you miss restart.
Note grenades are fairly rare and 3-4 enemies can overpower you even on easy. Use grenades sparingly on groups of 3 or more. Enemies by themselves or in groups of 2 are easy.