Use Iron Sights: Always use iron sights. This is the way to line up your shot properly. It increases your combat effectiveness and consequently your likely-hood to hit the target.
Breathe: Fire between breathing cycles. You CAN hear the inhaling and exhaling. Your combat effectiveness is highest after you finish inhaling or exhaling. Press the insert key to make the your breathing significantly less.
Stay Low: Crouch whenever possible. The lower you are, the more accurate your shots will be due to increased combat effectiveness.
Aim for the Center of Mass: Aim at the center of the target's body. Do not aim for the head. Aim one or two pixels to the left of the iron sight.
One Target, One Shot: You want to get one target with one shot. If you can pull off getting a target with the 2nd shot - DO IT. But be damn sure you can make it. Do not do this more than once. Remember, you only have 40 bullets for 40 targets. To be given a chance to do the Advanced Marksman training a score of 36 is required, which means you can only miss 4 targets.
Don't Use Left Mouse Button: Use your Ctrl button to fire, so you don't move your mouse when you click.
Right Mouse Button: Bind your right mouse button to your sights instead of Z so that you can easily zoom in and out to acquire a target.
Adjust Your Screen Resolution: Put you screen at the lowest resolution possible, so the targets will be a little bigger and easier to hit.
Press the "SHIFT" key to reduce your walking speed. This puts accuracy up quite a bit.