Batman started out killing, even if accidentally a couple of times. The pics here from Batman #1 show this quite clearly.
In one panel, looking through the sights of a plane's machine gun, he even says, "Much as I hate to take human life, I'm afraid this time it's necessary."
The monster he "accidentally" strangles with a noose from his Batplane and then says something about the monster probably being better off, and then he just cuts him loose. Whatever helps you sleep at night, Batman.
The other monster is knocked off the ledge by the Batplane, as a quick and tidy way to finish the story that went on too long.
Three deaths in the opener.