The Collaborative International Dictionary of English v.0.48:

Attainableness \At*tain"a*ble*ness\, n.
   The quality of being attainable; attainability.
   [1913 Webster]

WordNet (r) 3.0 (2006):

attainableness
    n 1: the state of being achievable [syn: achievability,
         attainability, attainableness]