There are 128 monsters in the first Final Fantasy, all of which you'll need to encounter and defeat if you want the achievement tied to 100% Bestiary completion. Here are all the beasts in the Final Fantasy 1 Pixel Remaster Bestiary and their locations.
Final Fantasy 1 Pixel Remaster Platinum Trophy Guide Part 1 The Beginning of It All
It took me 13 hours to complete Final Fantasy 1 Pixel Remaster, with 100% Bestiary completion being the last thing I needed. Due to the location of some of the final monsters, you cannot complete Bestiary until you have completed the game.
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If you need further assistance, check out our Final Fantasy 1 Pixel Remaster Walkthrough guide for a complete step-by-step overview of Final Fantasy 1 Pixel Remaster.