They've said in interviews that Robin isn't actually killing anyone.
Which goes into my biggest problem with the trailer. It just looks so poorly made. The editing is all over the place, the song choice is terrible, and they didn't try to do anything to sell the characters or story beyond the tone.
Everything about the dark tone....eh. Personally, I think the constant crying over the slightest hint of "darkness" or "grittiness" in properties like this is lame as fukk. One of the major appeals of superheroes is their malleability. Under the right hand, they can be dark or light or gritty or silly or whatever and still be the same characters. For example, "Batman: The Brave and the Bold" came out the same year as "The Dark Knight" and both are equally valid interpretations of that character. I was listening to the Double Toasted review of the trailer and they called out the new Sabrina series despite the fact that the comic it's based on is really good. Complaining about "darkness" is a lazy criticism and little more than a meme at this point.