He was capable of shaking off the criticism due to the fact that he believed strongly enough in himself, which I find quite remarkable.

shaking 是动词 shake 的现在分词形式，shake 本意是"摇动、震动"，在这里表示"摆脱"的动作。 off 是介词，表示"离开、脱离"的状态。 shaking off 是一个固定短语，字面意思是"通过摇动使某物脱落"，引申为"摆脱、甩掉"某种负面事物或影响。