This is story-related and cannot be missed.
You will earn this in the final Raccoon’s Destruction chapter. The ‘Pursuer’ is Nemesis. For the duration of the battle, shooting at his head is the best tactic. A few times he’ll attack you through the ground with tentacles. Even then, continue shooting him. Like with the Tyrant from the first scenario, grenades work surprisingly well against Nemesis. When you kill Nemesis you will earn the trophy and end the scenario.