The phrase "bore brunt of" usually means to bear the main force or consequence of a particular situation or action. Its antonyms would be "escape," "avoid," or "evade." When you escape the brunt of something, you have not experienced the full negative impact of an event or a decision. Avoiding the brunt of a problem means you have taken measures to stay clear from it, while evading it means you have skillfully dodged it. In a way, the antonyms for "bore brunt of" suggest a strategy to move away from difficult situations rather than take them head-on, which can be a prudent approach at times.