The Good Listener trophy in El Shaddai says I must
Obtain all of the Freemen's notes. If I happen to miss them in my first playthrough, can I just pick up the ones I missed in playthroughs on other difficulties, or do I have to hunt them all down in a single playthrough?
You don't have to collect them all in one single playthrough. You can select the chapter with the missing note from the menu and get it this way if you happen to have missed it in your first playthrough.
In fact there are no missable achievements/trophies in this game at all.