I would say it depends on the shapeshifter. More than one person went by the name Clayface and each had slight variations. 'He' tended to leave a film of clay behind him and was highly susceptible to heat, which made him melt, and water, which could kill him.
Some shapeshifters are better than others. Do they know the person they're impersonating? How much of them can they mimic? How long does it last? Someone who can only mimic a person on a surface level would be easier to catch than someone who could mimic a person's mind as well.