In the center of the main area where you find Greeneye, there is a Grenade Launcher on the ledge. That will be your best friend in this fight. Firing the grenade launcher on the side of Green Eye's body, assuming the grenade makes contact, will take out two green dots at a time. Once you get to the part with shooting Green Eye in the head, with the four red dots, fire a grenade to the center of the head. You will take out all 4 dots in one shot. HIs life should be like one shot left also, so just fire a rocket or some bullets to the head. The grenade is considerably more powerful than the rocket launcher. Make sure you stay on the move, and when going for the head, stay up on ledges, as he will constantly charge attach if your on the ground.