Max out Feendorf’s level, so you can buy a few “Exorcist's Peridot (superb)”, which reduces the chance of encounters by 100%. Next, make sure you are on one of the ends of the map (east or west), and set an expedition to the opposite end (try to avoid mountains, if you want to keep the expedition cheaper). When you are about to depart, the game will ask you if you want to use an item. Pick one of the “Exorcist's Peridot (superb)” you bought. Now do this a few more times and the trophy will be yours!