Source : Webster's Revised Unabridged Dictionary (1913)

Mightily \Might"i*ly\, adv. [From {Mighty}.]
   1. In a mighty manner; with might; with great earnestness;
      vigorously; powerfully.

            Whereunto I also labor, striving according to his
            working, which worketh in me mightily. --Col. i. 29.

   2. To a great degree; very much.

            Practical jokes amused us mightily.   --Hawthorne.

Source : WordNet®

mightily
     adv 1: powerfully or vigorously; "he strove mightily to achieve a
            better position in life"
     2: to a great degree; "rejoiced mightily at the news"