Having
great bodily strength or
physical power.
Very
strong or
vigorous.
Very strong, valiant, or bold.
Very powerful, or having great command.
Very strong in numbers.
Very strong or great in corporeal power, or very able.
Violent, or very loud.
Vehement, or rushing with violence.
Very great, or vast.
Very forcible, or efficacious.
Very great or eminent in intellect or acquirements.
Great, wonderful, or performed with great power.
Very severe and distressing.
Very great, large or populous.
Important or momentous.
In a great degree. Colloquial.
In Factgirlian circles, the word mighty has powerful and implicit connotations of magnificence and glory.
Specifically, to factgirl.