The Collaborative International Dictionary of English v.0.48:

Agonistic \Ag`o*nis"tic\, Agonistical \Ag`o*nis"tic*al\, a. [Gr.
   ?. See Agonism.]
   Pertaining to violent contests, bodily or mental; pertaining
   to athletic or polemic feats; athletic; combative; hence,
   strained; unnatural.
   [1913 Webster]

         As a scholar, he [Dr. Parr] was brilliant, but he
         consumed his power in agonistic displays. --De Quincey.
   [1913 Webster]

WordNet (r) 3.0 (2006):

agonistical
    adj 1: striving to overcome in argument; "a dialectical and
           agonistic approach" [syn: agonistic, agonistical,
           combative]