I wouldn’t call this an official guide for the trophy. Just came here looking to offer my own experience regarding kills being counted towards overall stats in the background.
I've seen lots of folks on other sites asking if their kills in Chapter and Encounter Select count for the overall 1000, since each time you start a new session all stats are automatically reset. Some people say they do count, while others say they only got it when they started a new game and chose the option to carry over stats. There is very little to no information from the aspect of only continuing to perform kills in chapter or encounter select (as far as I could find in my many searches).
I can confirm that as of March 17, 2018, your kills in Chapter Select and Encounter Select do count towards your overall 1000 kills for this trophy. I have the current version of the game as of this date, which is 1.32.
I completed the game on Moderate, and finished with about 550- 600 kills. After I completed the game, I did various kill-type trophies via the chapter and encounter select method only (rope kills, ledge kills, hip fire kills, 100 without dying, etc.). All of the kills from those other trophies ended up counting. I never started a new game that carried over stats. Each time I did one of the chapter or encounter select sessions, my stats always reset, but the game kept counting the overall number in the background.
After I got the trophy for 100 kills without dying (using the Ballroom encounter of Chapter 7), I calculated I was at about 900-950 kills after finishing the game and doing the other kill trophies. After the 100-kill trophy popped, I kept going (in that same encounter) to see if I could trigger the 1,000 kill one. After about 5 more minutes of killing the infinite spawn enemies on the ledges outside, I got the trophy.
Hope this helps anyone looking for clarification.