[JimmyPlacid]

Well, as i stated 16 months ago (2nd post in this thread) it is necessary to gain stars to make more enemies appear. When you kill more than 50 % of the enemies in a stage you will gain a star, if you die you will lose a star. Same goes for the 300 Climax Kills, more stars --> more enemies ---> more kills. You already got many of the medals, so i guess you already know that you should use Climax in small bursts, so it is reloaded faster.
Back to the 800 kills:
In my opinion it is absolutely necessary to get to special stage 10. You need to have at least 4 stars + gaining one at the end of stage 9 to get access. In that stage is a huge amount of targets and no one is shooting at you. The difference between "normal" stage 10 and the special one should be at least 100 kills.

Edit: Dont hold the brake, you will get shot down if you do and lose a star.