This achievement is obtained by killing 250 Zombies with blunt weapons. You'll probably get this achievement early on if you use a blunt weapon specialist like Sam B, but it can be obtained by any character using a blunt weapon. Blunt weapons can easily be identified by their Icon so there shouldn't be any confusion as to which weapons can be used for this achievement.
Solution Update: Thanks to Hirsute Dave for reminding me that this and all zombie killing achievements stack across all your character playthroughs. You can do the first few quests on a couple of characters and they will all rack up the counter.