I would suggest you use the pistol or some other slow firing weapon so that you don't accidentally shoot some extra bullets after killing the enemy. The first level of the game is the easiest in terms of getting swarmed. Take it slow and get as many hits as you can with a relatively low powered weapon. This way you can get a couple of shots on 1 enemy to increase your accuracy percentage without having to put yourself into any sticky situations. The best thing you can do is take it slow and be careful with your trigger finger.
Complete a level with accuracy rating of 90% or higher with 300 or more bullets fired