Mission: Throttle
This trophy opportunity takes place right at the very beginning of the level, so you can always try again from the main menu if you have problems.
The easiest way to get this is just to hold down your machine guns, and DO NOT use your missiles. You will have to aim at enemy ships which will show up as red diamonds on your HUD. Use your air brake in order to go more slowly as well! Make your way through the canyon, and focus on killing as many enemies as possible using those machine guns. If you get to 10, the trophy will unlock but if you get to the end you can reload your last checkpoint or restart the entire mission.