A) is the best answer but I would say "campaigning group"
The question is whether it's a compound noun or an adjective + noun. Since 'campaign group' is an atypical compound noun, it would need to stand on its own
"Greenpeace is a campaign group"
But as soon as you add the adjective environmental, the atypical nature of the compound noun loses validity and the adjective 'campaigning' should be used to describe the noun.
"Greenpeace is an independent global campaigning network"
The second one is how they actually describe themselves on themselves on their own website.