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 的基本意思是"摇动、抖动"。 off 在这里用作副词，表示"离开、摆脱"的状态。 shake off 是一个短语动词，字面意思是"抖落"，引申为"摆脱（负面事物）"的意思，在这里指摆脱批评的影响。