I've finished this game before and not gotten the badge, and the first time I finished it today, I still didn't get the badge. Both times, I made a point of getting all the pictures and items. When it didn't award today, I went back for a speed run, just getting the candles and the required ghost and getting out. It took about 5 minutes, and I got the badge.
tl;dr: If you're not getting the badge, try finishing the game as fast as you can, without worrying about all getting all the stuff.
 "Socrates Jones: Pro Philosopher"){kind=icon}
 "Ghostscape"){kind=icon}