The Details on Batman Related Deaths in Detective Comics Pre and Post Robin.

There were eleven issues of Detective Comics (May 1939-March 1940) before Robin's appearance.  Batman kills his enemies, and the occasional henchman, in eight of them. Batman also repeatedly shows no remorse for causing the deaths of his enemies. This means somebody (henchman or antagonist) was getting killed in 72% of the stories.

• Detective Comics #27  - Batman punches Mr. Stryker into a vat of acid, as Mr. Stryker takes a shot at him. Afterwards Batman notes: "A fitting end for his kind."
• Detective Comics #28 - Batman kicks a thug off the roof of a tall building, later the narrator notes "The body of the man that went over the roof has attracted the police," implying his death.
• Detective Comics #30 - Batman snaps a "Cossack's" neck with a kick.
• Detective Comics #32 - Batman shoots two vampires in order to kill them and free his girlfriend from their control.
• Detective Comics #33 - Batman knocks out a guard to escape, and then puts his Batman costume on the guard, knowing the antagonist is going to (and does) execute Batman, leading to the guard's death. Elsewhere, the primary antagonist is killed in a plane crash caused by his fight with Batman. The first is my personal favorite, because Batman really didn't need to put his costume on the guard once he had been subdued.
• Detective Comics #34 - Antagonist, the Duc D'Orterre, is killed in a car crash in a fight with Batman.
• Detective Comics #35 - Batman knocks the antagonist, Mr. Lenox, out the window of a tall building. "With bitter irony, across the crushed body falls the blood-red idol, Kila, God of Destruction!"He also punches a Chinese swordsman onto another swordsman's sword.
• Detective Comics #37 - Batman kills a 'foreign agent' by punching him onto a sword stuck through a door.

Total of 8 Batman stories where somebody dies due to Batman's involvement.

There was an interesting transitional phase after Robin appeared. Batman still killed people but it was in a less direct way. To understand the difference in the comics that occurred with the appearance of Robin, look at the difference between the eleven issues of Detective Comics after Robin's introduction and the eleven issues that were published before Robin. Deaths trailed off after Robin appeared, but at the same time Batman was still definitely killing people.

• In Detective Comics #39 Batman pushes a statue onto six swordsmen and it is stated that they are killed.
• In Detective Comics #42 Batman & Robin's exposure of a plot leads the antagonist to shoot himself in the head in front of them.
• In Detective Comics #46 Batman punches Hugo Strange into a deep ravine, where he "Topples to his Doom."

A total of 3 Batman stories with explicit killing.