After the first shoot-out you will be instructed to rescue Pegorino from the Pavanos. Instead of entering the warehouse where all the assailants are waiting to attack, go up the concrete steps and make a mad-dash (change weapon to pistol or fist so that you can sprint) along the outside wall of the building (the wide open paved area). You will be shot at, but it should be possible to get to Jimmy even with 1/4 health remaining. When you get to the rear of the warehouse Jimmy is slumped against a wall.
So, you can complete that part of the mission without firing a single shot!
After the scripted car chase there is a health pack on the ground where the Pavanos car crashes.
Hope this helps