This trophy is not as hard to unlock as it sounds. Auto-reloading occurs when you shoot your clip empty and Nathan will automatically reload the weapon.
All you need to do is remember to hit R2 to reload your weapon before the clip is empty, which should be pretty standard practice for anyone experienced in FPS and TPS games.
You can switch weapons as often as you like, and you can even empty a weapons clip completely as long as you have no ammo left to auto-reload it with. Your best bet is to stick with high-capacity clip automatic rifles until you unlock the trophy.
Note: The trophy will unlock right away after the 50th kill in this manner.