The Collaborative International Dictionary of English v.0.48:

Onset \On"set`\, n. [On + set.]
   1. A rushing or setting upon; an attack; an assault; a
      storming; especially, the assault of an army. --Milton.
      [1913 Webster]

            The onset and retire
            Of both your armies.                  --Shak.
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            Who on that day the word of onset gave.
                                                  --Wordsworth.
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   2. A setting about; a beginning; -- used especially of
      diseases or pathological symptoms. --Shak.
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            There is surely no greater wisdom than well to time
            the beginnings and onsets of things.  --Bacon.
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   3. Anything set on, or added, as an ornament or as a useful
      appendage. [Obs.] --Johnson.
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The Collaborative International Dictionary of English v.0.48:

Onset \On"set`\, v. t.
   1. To assault; to set upon. [Obs.]
      [1913 Webster]

   2. To set about; to begin. [Obs.] --Carew.
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WordNet (r) 3.0 (2006):

onset
    n 1: the beginning or early stages; "the onset of pneumonia"
         [syn: onset, oncoming]
    2: (military) an offensive against an enemy (using weapons);
       "the attack began at dawn" [syn: attack, onslaught,
       onset, onrush]