The Collaborative International Dictionary of English v.0.48:

Intrepidly \In*trep"id*ly\, adv.
   In an intrepid manner; courageously; resolutely.
   [1913 Webster]

WordNet (r) 3.0 (2006):

intrepidly
    adv 1: without fear; "fearlessly, he led the troops into combat"
           [syn: fearlessly, dauntlessly, intrepidly] [ant:
           fearfully]

Moby Thesaurus II by Grady Ward, 1.0:

29 Moby Thesaurus words for "intrepidly":
   audaciously, boldly, bravely, bulldoggishly, chivalrously,
   courageously, daringly, doughtily, fearlessly, gallantly, gamely,
   gutsily, hardily, heroically, knightly, like a man, like a soldier,
   pertinaciously, pluckily, resolutely, spunkily, stalwartly,
   stoutly, tenaciously, unfearfully, unfearingly, valiantly,
   valorously, yeomanly