There are many videos and pictures that show actual monsters HP, but it seems there is nothing in the game settings about that.
Zelda: Breath of the Wild – How to Display Enemy HP
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Best Answer
Certain outfits have special effects beyond just improving your defense. One of the effects of the Champion's Shirt is that it reveals the numerical Monster HP.
To get the Champion's Shirt, you need to complete a single memory quest for Impa in Kakariko Village.