Keep track of your progress by going into Titles > Gameplay record > Small Yokai - Large Yokai.
Only the base-game enemies count, DLC-specific enemies may appear on this list but are not needed to unlock the Trophy.
Once you have the following done at least once, the trophy will unlock;
Small Yokai
Dwellers
Skeleton Warriors
Oni-bi
Biwa Boku-boku
Sentries
Spiders
Lesser Umi-bozu
Mudmen
Karakasa Umbrellas
Kappa
Mujina
Nurikabe
Fiends
Amrita Fiends
One-Eyed Imps
One-Eyed Oni
Onyudo
Wheelmonks
Flying Bolts
Karasu Tengu
*Mujina are found in Mimic chests, Nurikabe are the walls with eyes
Large Yokai
Onryoki
Hino-enma
Nue
Great Centipedes
Umi-bozu
Joro-gumo
Yuki-onna
White Tiger
Giant Frogs
Ogresses
Gasha-dokuro
Yamata-no-Orochi
Hundred Eyes