What emotion is the 'Mad Scientist' showing when they say "I'll show them all!"
You could say they are feeling vindictive or are characterized by vindictiveness.
Vindictive
a : disposed to seek revenge : vengeful
b : intended for or involving revenge
- Merriam-Webster
An example of the word can be found in this column by Charles Krauthammer:
Trump relishes such a cat-and-mouse game and, by playing it so openly, reveals a deeply repellent vindictiveness in the service of a pathological need to display dominance.
Hubris. "Exaggerated pride." Merriam-Webster.
I think that vengefulness could do.
The mad scientists is showing vengefulness.