The Slasher kill bonus is achieved when you kill someone by means of a Katana. This kill bonus is easy to achieve due to the high level of damage inflicted by the Katana. Of course, there are the problems of getting in range. Spiral Chamber will affect the range greatly, so much that you can kill someone when they are at the bottom of the speed platform, and you are halfway down, J.Rockit is an expert on this kill bonus.
Note: If your enemy is firing on you when you crack his skull, you'll get Reflection instead. This often happens to be the case.