The easiest way to do this is in Endless Hell Mode. It may take you a try or two, but if you get a good run, getting constant powerups, then you should easily be able to get 7000 points.
Just try to mostly stay in middle, picking up powerups to get suped-up so you kill fast enough to keep the combo going.
You should hit 7,000 around level 8, surely in Level 9.
I found the best power-ups are the ones that give you a wide-angle shot, it looks like a triangle that crisscrosses at the top. Also sometimes I am just not getting a power up I need, like the wide angle, try and grab the power up that kills everything on the screen, it's a straight row of rectangles.
Sometimes you just get unlucky and don't get good enough power-up drops, but it's just RNG, you will get this achievement in 2 or 3 tries if not your very first.