鞭挞 is literary/written register. In speech you'd say 批评 (criticize) or 痛斥 (denounce). It carries an image of moral whipping - common in book reviews, editorials and political rhetoric.
memory
鞭 = whip, 挞 = to beat with a stick. Both characters mean 'to strike with a flexible weapon', so 鞭挞 stacks the imagery: literal whipping -> figurative verbal lashing.
