I completed the similar challenge with the rifle while shooting at the queen in the final level. Stands to reason that the pistol challenge would unlock similarly. I'll have to confirm once I get to that challenge, though...
No offence guys, but there's some horrible advice in this topic!
Johnnycigar has a solid method though - I used that part of the campaign to complete both the 'full clip don't miss' challenges. Put the silencer on the pistol and make sure not to use high velocity rounds and you can put several more into each enemy before they die.
I could not get this challenge by firing every round into the Queen - that's what I tried first before heading back to chapter 2