Intellectual Pursuits asks for Story exactly: set it on the first run or it costs you a playthrough
Two independent difficulties, action and puzzles, and only one of the four accepts "or higher". The easy-puzzle trophy is held by fewer people than the hard one, and that fact explains how to plan the runs.
And it counts towards Grateful for a Worthy Foe, Intellectual Pursuits, Wise Researcher, required for the platinum.
"Or higher" appears in only two of the four
Silent Hill f separates action difficulty and puzzle difficulty, and sets them independently. The four trophies split between the two, but not all of them accept the "or higher" wording, and that is where all the planning lives.
Thankful to Be Here — 65.13%. Finish the game with action difficulty on Story or higher.
It lands on its own during your first run with nothing special required. That 65.13% is precisely the number of people who finish Silent Hill f once, so it serves as the benchmark for reading every other percentage on the list.
Grateful for a Worthy Foe — 31.98%. Finish the game with action difficulty on Hard or higher.
The "or higher" wording is the key: if you do the third run on Lost in the Fog, this one pops by itself and saves you a whole playthrough. Do not do it separately.
Wise Researcher — 53.38%. Finish the game with puzzle difficulty on Hard. This is the second run's.
More than half of all players hold it, and more people than hold the Story one: most players start the game right here.
Intellectual Pursuits — 39.38%. Finish the game with puzzle difficulty on Story.
Careful: this one asks for Story exactly, and does not accept "or higher".
Intellectual Pursuits asks for puzzle difficulty on Story exactly. There is no "or higher": start on Hard and you need an extra run for this trophy alone.
Fewer people hold the easy one than the hard one
There is an oddity here that throws off anyone skimming the list: Intellectual Pursuits (39.38%) is held by fewer people than Wise Researcher (53.38%). The easy-puzzle trophy is rarer than the hard-puzzle one, fourteen points below it.
The reason has nothing to do with difficulty: almost nobody plays their first run with puzzles on easy. Most start on Hard straight away, take Wise Researcher without thinking, and only afterwards discover the Story one is missing.
Leaving it for last costs an extra run for this alone. It is Silent Hill f's most expensive planning mistake, and the only one that cannot be fixed by changing difficulty mid-run.
The split that costs the fewest runs:
First run. Action on Story and puzzles on Story: this takes Thankful to Be Here and Intellectual Pursuits. It is the learning run, and clearing the easy-puzzle trophy here is what saves the extra playthrough.
Second run. Puzzles on Hard for Wise Researcher. Action difficulty does not matter on this one.
Third run. Action on Lost in the Fog, which through "or higher" awards Grateful for a Worthy Foe with no run dedicated to Hard.
Three runs, four difficulty trophies, no playthrough spent purely on raising a setting. And those same three runs are the ones the endings require, so the difficulty block adds no runs at all when planned from the start.
The trophies involved
Each one links to its section inside the full Silent Hill f trophy guide.