Finally got started on this. Playing through on the Warrior difficulty. Completed chapters 1 and 2.
I would have probably completed chapter 3 as well had I not completed chapter 2 a second time. Yeah, that's right--twice. There's a trophy for completing chapter 1, so I assumed there would be a trophy for completing chapter 2. But I didn't get one. I thought perhaps it didn't award the trophy because I created a new save upon completion. So I ran the chapter again, this time encountering hellish frustration with the boss which made little sense considering the first time through he was little trouble, overwrote chapter 1's clear data... and still didn't get my trophy. I'm now going to assume (read: hope) there is NOT a trophy awarded after each chapter completion. Otherwise, the game hands out trophies like candy as you "learn" various abilities.