- On having killed the guard he dragged him into the bushes.
- Having killed the guard he dragged him into the bushes.
What is the difference between them?
It indicates that killing the guard prompted you to hide his body - you killed him and immediately knew to hide his body.
If he killed the guard, and was content leaving him in the open, started creeping away... but then heard more guards approaching - then that would be the prompt for hiding the body, not killing him, so you'd use having killed the guard, he dragged him into the bushes.
Of course if you've recently informed the reader that he killed the guard, avoid repeating yourself with something like he dragged the corpse into the bushes.