The Collaborative International Dictionary of English v.0.48:

Attainment \At*tain"ment\, n.
   1. The act of attaining; the act of arriving at or reaching;
      hence, the act of obtaining by efforts.
      [1913 Webster]

            The attainment of every desired object. --Sir W.
                                                  Jones.
      [1913 Webster]

   2. That which is attained to, or obtained by exertion;
      acquirement; acquisition; (pl.), mental acquirements;
      knowledge; as, literary and scientific attainments.
      [1913 Webster]

WordNet (r) 3.0 (2006):

attainment
    n 1: the act of achieving an aim; "the attainment of
         independence"
    2: arrival at a new stage; "his attainment of puberty was
       delayed by malnutrition"
    3: an ability that has been acquired by training [syn: skill,
       accomplishment, acquirement, acquisition, attainment]

Moby Thesaurus II by Grady Ward, 1.0:

61 Moby Thesaurus words for "attainment":
   accession, accomplished fact, accomplishment, accomplishments,
   achievement, acquirement, acquisition, acquisition of knowledge,
   acquisitions, addition, advent, appearance, approach, arrival,
   attainments, carrying out, coming, coming by, consummation,
   discharge, dispatch, dragging down, earnings, edification,
   education, effectuation, enlightenment, execution, fait accompli,
   finish, fruition, fulfillment, gaining, getting, getting hold of,
   illumination, implementation, instruction, learning,
   liberal education, making, mission accomplished, moneygetting,
   moneygrubbing, moneymaking, obtainment, obtention, performance,
   procural, procurance, procuration, procurement, production,
   reaching, realization, securement, sophistication,
   store of knowledge, success, trover, winning