The Collaborative International Dictionary of English v.0.48:

Mightily \Might"i*ly\, adv. [From Mighty.]
   1. In a mighty manner; with might; with great earnestness;
      vigorously; powerfully.
      [1913 Webster]

            Whereunto I also labor, striving according to his
            working, which worketh in me mightily. --Col. i. 29.
      [1913 Webster]

   2. To a great degree; very much.
      [1913 Webster]

            Practical jokes amused us mightily.   --Hawthorne.
      [1913 Webster]

WordNet (r) 3.0 (2006):

mightily
    adv 1: powerfully or vigorously; "he strove mightily to achieve
           a better position in life"
    2: (Southern regional intensive) very; to a great degree; "the
       baby is mighty cute"; "he's mighty tired"; "it is powerful
       humid"; "that boy is powerful big now"; "they have a right
       nice place"; "they rejoiced mightily" [syn: mighty,
       mightily, powerful, right]

Moby Thesaurus II by Grady Ward, 1.0:

78 Moby Thesaurus words for "mightily":
   almighty, arduously, authoritatively, awfully, big, cogently,
   commandingly, consequentially, deafeningly, dynamically,
   effectively, effectually, energetically, ex cathedra, exceedingly,
   extremely, firmly, forcefully, forcibly, greatly, hardly, heartily,
   highly, hugely, imperatively, imperviously, impregnably, intensely,
   invincibly, invulnerably, irresistibly, just, laboriously, loudly,
   lustily, might and main, mighty, momentously, notably, officially,
   only too, potently, powerful, powerfully, pretty, productively,
   puissantly, pungently, quite, real, really, resistantly, right,
   robustly, ruggedly, so, soundly, stalwartly, staunchly, stoutly,
   strenuously, strikingly, strongly, sturdily, surpassingly,
   tellingly, terribly, terrifically, to good account,
   to good purpose, toilsomely, unyieldingly, very, vigorously,
   weightily, with a vengeance, with authority, with telling effect