To answer your questions:
1. Biodiversity and conservation aren't areas that business consultancies service. (Ask yourself - where is the money?) You will, however, find some overlap in the environmental/sustainability/renewables service lines: see PwC's Sustainability practice, for example. Some of the infrastructure and engineering consultancies, and international development consultancies too. You will also find small environmental consultancies when you start googling...
2. As Telson correctly says, you'll join at the bottom of the food chain. You'll have to learn how to consult, and unless you have any significant work experience to offer, you'll do consultancy boot camp just like everyone else.
I suspect you'll have more luck exploring openings in social enterprise foundations and impact funds.