I've only gotten a Platinum for three games so far (inFamous 1, Heavy Rain, and Final Fantasy XIII), but FFXIII was by far the most time consuming. I ended up defeating the Long Gui for my last trophy because I had trouble defeating it the legit way (I ended up knocking it down with a summon, debuff it, stagger it once, spam Death on it before it stands right up).

I think I also remember the time when I defeated the final boss in Oath of Felghana on Normal on my first try. To this day, I don't know how I managed to pull that one off.