Unlike Danganronpa 2, there are no instructions about the Hidden Monokuma so you will need to open your eyes and keep a lookout for them. (V3 for me has too many things on the screen so it really strain my eyes while looking for them.)
Chapter 1 Location
School Building 1F
Near the School Store & Dining Hall, on the path towards the Gym, you can see it dancing on the table
Courtyard
On the bench outside the dormitory
Game Room
On the right side near the red gaming machine (it is quite small)
School Building 1F – Girls Toilet
On top of the first sink
Class Trial – Hangman Game
You can find it in one of the orbs.
Chapter 2 Location
3F near Ultimate Child Caregiver Lab
Under a bench in the big open space area
Courtyard
On the grass behind the fence on the way leading to the Dining Hall
Ultimate Inventor Lab
In the middle of the room
Warehouse
On the shelf with the red strips boxes
Class Trial – Psyche Taxi
During 3rd question, on the road (right lane)
Chapter 3 Location
Courtyard
In front of the red door
Boiler Room
In the middle of the room on the floor
Ultimate Pianist Lab
In front of the piano
Casino Area
Near the hotel on the right side of the spotlights, you can see Monokuma catwalk-ing on the grass
Class Trial – Mind Mine
Remember to unreveal Monokuma before completing the mind mine
Chapter 4 Location
Dormitory
On the staircase at the boy’s side of the room
Ultimate Akido Master’s Lab
Right at the entrance
Basement
On the desk next to the stairs
School Building 2F
Along the Hallway from the Ultimate Maid Lab towards the Ultimate Entomologist Lab, you can find Monokuma on the ledge
Class Trial – Hangman Gambit (2nd)
You can find it in one of the orbs
Chapter 5 Location
4F Hallway
In front of the stairs with the Shrine Gate, on top of one of the headless statue
5F Hallway
Outside the Ultimate Detective Lab
Ultimate Cosplayer Lab
On top of the filming set on the left of the room
Ultimate Robot Lab
In the center of the room
Class Trial – Psyche Taxi
Question 2 on the left lane
Chapter 6 Location
Courtyard
Along that path after the pool
1F School Building
On the right, behind the center of the doorway where the ceiling has fallen
5F School Building
On the ledge of the stairs
Ultimate Astronaut Lab
around 4F of the spiral staircase, on the middle ledge
Class Trial – Mind Mine
Remember to unreveal Monokuma before completing the mind mine