Yay! Finally unlocked this last night!
I've only played this game on roughly 12 occasions - when it is has coincided with a Calendar Man day. Each time, I'd make a bit more progress in the game as well, until now...I'm right at the end!
I did have to go "offline" for two of the dates, when I happened to be away from my console on those days, but otherwise, every other date was legit.
Now looking forward to completing the game.