This has to be done in one run.
There are three enemy types that randomly appear in levels: Bats, Mummies, and Snakes. The usual way to get past them is to find single use Arrows (or rarely the Machete) to kill them.
To unlock this achievement, you must kill five Bats without killing any Mummies or Snakes. Should a Snake or Mummy be blocking your path, you'll have to use Dynamite to blast through a wall to get around them so that you don't kill them.