Regarding "clamp down" and "fight against", you could say them.
More natural would be:
"We need to do something about school bullying."; "We need to stop this bullying at school." (The fact that it is a problem and needs combatting is understood in this case.)
"We need to institute a plan to combat school bullying." - This is more formal, and starts getting into the realm of written policies, rather than merely verbal suggestions.