Excessively conceited (5)
(Other definitions for cocky that I've seen before include "Made observation" , "Boldly conceited" , "Cheekily self-assured" , "Self-important, conceited" , "Impudently self-assured" .)
(Other definitions for vainglorious that I've seen before include "Cocky" , "Boastful; rousing viola (anag.)" , "Excessively self-proud" , "Self-important -- savouring oil (anag)" , "Excessively self-important" .)