The phrase "to fight the fight" means to engage in a struggle or battle, typically against something difficult or challenging, and to give one's best effort to overcome it. Full definition
The participants, especially some who have been fighting this fight for decades, deserve credit for their patience and persistence in what appears likely to be a long campaign. (sciencemag.org)
It would allow consumers facing trolls to put litigation on hold while the suppliers and manufacturers of products and services at issue fight the fight at hand. (eff.org)