The Collaborative International Dictionary of English v.0.48:

Achieve \A*chieve"\, v. t. [imp. & p. p. Achieved; p. pr. &
   vb. n. Achieving.] [OE. acheven, OF. achever, achiever, F.
   achever, to finish; [`a] (L. ad) + OF. chief, F. chef, end,
   head, fr. L. caput head. See Chief.]
   1. To carry on to a final close; to bring out into a
      perfected state; to accomplish; to perform; -- as, to
      achieve a feat, an exploit, an enterprise.
      [1913 Webster]

            Supposing faculties and powers to be the same, far
            more may be achieved in any line by the aid of a
            capital, invigorating motive than without it. --I.
                                                  Taylor.
      [1913 Webster]

   2. To obtain, or gain, as the result of exertion; to succeed
      in gaining; to win.
      [1913 Webster]

            Some are born great, some achieve greatness. --Shak.
      [1913 Webster]

            Thou hast achieved our liberty.       --Milton.
      [1913 Webster]

   Note: [[Obs]., with a material thing as the aim.]
         [1913 Webster]

               Show all the spoils by valiant kings achieved.
                                                  --Prior.
         [1913 Webster]

               He hath achieved a maid
               That paragons description.         --Shak.
         [1913 Webster]

   3. To finish; to kill. [Obs.] --Shak.
      [1913 Webster]

   Syn: To accomplish; effect; fulfill; complete; execute;
        perform; realize; obtain. See Accomplish.
        [1913 Webster]

WordNet (r) 3.0 (2006):

achieve
    v 1: to gain with effort; "she achieved her goal despite
         setbacks" [syn: achieve, accomplish, attain, reach]

Moby Thesaurus II by Grady Ward, 1.0:

109 Moby Thesaurus words for "achieve":
   accomplish, acquire, act, actualize, approach, arrive, arrive at,
   arrive in, attain, attain to, be productive, be received, blow in,
   bob up, bring about, bring into being, bring off, bring through,
   bring to fruition, bring to pass, carry off, carry out, cause,
   check in, clock in, come, come in, come to, come to hand, commit,
   compass, complete, conclude, conquer, consummate,
   crown with success, deal with, discharge, dispatch, dispose of, do,
   do the job, do the trick, do to, effect, effectuate, enact,
   engineer, execute, fetch, fetch up at, find, finish, fulfill, gain,
   get, get by, get in, get there, get to, go and do, hit, hit town,
   industrialize, inflict, knock off, make, make it, manage,
   mass-produce, obtain, overcome, overproduce, pay, perform,
   perpetrate, polish off, pop up, produce, pull in, pull off,
   punch in, put across, put away, put over, put through, reach,
   realize, render, ring in, roll in, score, secure, show up, sign in,
   succeed, succeed in, surmount, take and do, take care of, time in,
   turn the trick, turn up, up and do, volume-produce, win, work,
   work out, wreak