I don't like it much. Being called Year Two invites suicidal comparisons with Miller and Mazzucchelli's Year One, but I'd have disliked it under any title.
The story has three main elements:
(a) a vigilante from twenty years ago, called the Reaper. Why's he returned now? Don't know, don't care. He's fairly dull and he kills people.
(b) Rachel Caspian, a charity worker and aspiring nun. She's a love interest for Batman, but her father is (unbeknownst to anyone) secretly the Reaper. I didn't care. At all. I was practically skipping over those pages. There are Venusian slime pools who were only born a few minutes ago, but already know where Rachel's subplot is going.
(c) Joe Chill, whose subplot is actually quite good. He's the guy who killed Bruce Wayne's parents twenty years ago and is now a top-class gang hitman who teams up with Batman to fight the Reaper. Imagine Batman's feelings about that. There's nothing even remotely surprising here, but there's some emotional weight in seeing these two working together.
Other, less important, story elements include:
(d) Leslie Thompkins, who appears to be important somehow. We're not told how and we're given no reason to be interested. She's just a white-haired lady who hangs around Bruce and knows some of his secrets. She seems nice, but she makes no difference to anything.
(e) Gordon, who's a bit stupid here.
I don't hate this story, but I was surprised on rereading to see how many of its elements were dead on arrival. The first big Reaper-Batman fight's a flop. Somehow, it's underwhelming. Every scene with Rachel. Gordon snapping his pipe, saying "looks like we were both wrong".
There was an editorial screw-up with the artists. Batman had been Alan Davis's big American break, but he quit after the first issue of this four-parter. Mike Barr wanted Chill to have a big gun and specified a Mauser with an extended barrel. Unfortunately, though, David Mazzucchelli gave Chill a smaller gun with no extended barrel in Year One. Davis refused to change his artwork and quit. Dick Giordano redrew the gun and Todd McFarlane drew the remaining three issues. (Mind you, Davis returned for Mike Barr's 1991 sequel, Full Circle.)
I don't mind the very different art styles. Davis and McFarlane could never be mistaken for each other, but that's fine and it works. What did jar was the ever-changing lettering. Four issues, four different letterers. Richard Starkings, Agustin Mas, John Costanza and Todd Klein. The Starkings-Mas transition is the really distracting one.
What's curious about this boring story is how close it gets to being good. I like Mike Barr, who also wrote Camelot 3000. Theoretically, both the Reaper and Rachel get strong character beats. Rachel had been going to become a nun and of course that ends up being her final choice, even though she'd already accepted a marriage proposal from Bruce Wayne. The Reaper is the older generation, with both Batman and Rachel representing the younger generation but in very different ways. This is a story that should have been worth telling. In the world of superhero comic books, you'd expect it to be above average. Somewhere between synopsis and the finished pages, though, things fell apart.
Thinking about it, its problem is that it's predictable. Its subplots and character choices all needed one more twist.