It's a one-shot sequel to Year Two, which to my surprise I remembered I also owned. It's an improvement, but still dumb.
Joe Chill's son (Joseph) comes back to plug the costumed hero who killed his father, so he... er, dresses up as the guy and murders some prostitutes for verisimilitude. Thank you, Jack the Ripper. No, Batman didn't chill Chill. It was the Reaper and Joseph was watching it all, but he still wants to kill Batman anyway. Well, fair enough. Wanting to kill Batman is sort of default Gotham City behaviour.
Oh, and Joseph? Your dad was a gangland hit man. Occupational hazard and so on. Just saying.
Now, the important thing is that there's nothing supervillainy about the Chills. They're just ordinary people. A bit thuggish, a bit stupid. Joseph didn't even know his dad until shortly before the latter died and hadn't even known for sure he was a criminal... and yet now, not many years later, he's capable of holding his own in a fist fight with Batman. Then, on capturing him, he builds an over-elaborate deathtrap for Batman and leaves silly clues to help our heroes find him. Nope, sorry. I didn't believe it. Joseph Chill never seemed like the kind of Adam West villain who'd do all that, with that deathtrap being the final straw. Gun to unconscious man's head, blam. End of problem. Oh, and the dialogue's occasionally a bit clunky, even before we start discussing Robin's painful quips (e.g. "surf's up, dudes") in his action scenes. When he's in the tights, I wanted him dead. When he's depressed because Batman's grounded him, though, he's okay.
That said, though, the story's basically okay if you can buy Joseph Chill's characterisation. That's an improvement on Year Two. Rachel's plot role is fine, despite its unflattering assumptions about her intelligence. (Interesting image change for a nun.) Batman's cool. ("You ought to have this place inspected.") The fratricide/sororicide scene is good. The Batman/Robin character journey is predictable, but does its job. In hindsight, this story's existence improves Year Two.