The Collaborative International Dictionary of English v.0.48:

Highflying \High"fly`ing\, a.
   1. Extravagant in opinions or ambition. "Highflying,
      arbitrary kings." --Dryden.
      [1913 Webster]

   2. Flying at a high altitude; -- of airplanes.
      [PJC]

   3. Having an excessively high cost or perceived value;
      temporarily very successful; -- of objects with respect to
      a market and people in their occupations; as, highflying
      internet stocks; highflying executives moving between
      companies.
      [PJC]

WordNet (r) 3.0 (2006):

highflying
    adj 1: moving upward or along at a considerable height; "some
           highflying fighter pilot fired a cannon shell into it"
    2: extravagant or ambitious or extreme in aims or opinions;
       "they did not understand what had happend at the once
       highflying company"