WordWeb Online

1. In an unpleasantly offensive manner
   "he smelled offensively unwashed"
    
2. In an obnoxious manner
   "he said so in one of his more offensively intellectually arrogant sentences"
   - objectionably, obnoxiously
    
3. In an aggressive manner
   "'In this crisis, we must act offensively,' the President said"; "the admiral intends to act offensively in the Mediterranean"

See also: offensive

Antonym: defensively, inoffensively