Political rivals tried to undermine his integrity with scandals.

undermine 由前缀 under-（表示"在...下面"）和动词 mine（挖矿、挖掘）组成，字面意思是"从下面挖"，引申为"暗中破坏、逐渐削弱"的意思。在句中指通过制造丑闻来暗中破坏他的诚信形象。