Start off on the first level, it doesn't matter what difficulty you're on.

When you go to Captain Keyes, when he gives you the magnum, you have to immediately turn and run for the door.

If you do it correctly, instead of getting a checkpoint, you just run through.

Once you do that grab 2 guns and run back and get the checkpoint.

When you go back to finish the mission, the Grunts appear and it will automatically pull up your pistol.

Now you have 3 weapons