This is a story achievement that will come at the end of the DLC during the final mission. After holding off waves of snipers and enemy soldiers, Putnam will arrive on the scene and hold a hostage in front of him. There will be other common soldiers flanking him, but the short timer suggests that you should probably ignore them. How I "defeated" Putnam was simply to have the eagle spirit selected, target Putnam with it, and attack by hitting Y. It's an unblockable and simple attack that gets the job done, and you don't have to deal with the common bad guys.