Collocations for damaging - adj.

be, prove
become

extremely, fairly, very, etc.
deeply (esp. BrE), highly, immensely (esp. BrE), profoundly, seriously, severely
This scandal could prove seriously damaging to the government.

possibly, potentially
economically, environmentally, politically, psychologically
Building the proposed new road would be environmentally damaging.

to
Smoking is damaging to health.

Damaging is used with these nouns:
allegation, consequence, criticism, dispute, effect, impact, radiation, ray, split, strike