This achievement will test your patience more than your skill. It is frustrating to no end. I went through two 360 controllers and a cat trying to get this achievement (just kidding about the controllers). As Codster2005 said, the asteroids are random and their is luck involved. Also, I am writing this assuming you've already played the ADS Cannon and are familiar with the controls and sizes of the asteroids.
The large asteroids do more damage than smaller ones. The large asteroids also break up into smaller asteroids. There are some fast moving medium-sized asteroids that do a lot of damage as well. These are your primary target because they move so fast and are the most dangerous asteroid in the bunch, so shoot them a.s.a.p.
Here are a few things I did that helped me out:
-Turn the brightness up on the game and your TV/monitor. This allows you to see the asteroids a LONG time before you can running the game's recommended brightness. I had the game brightness on full and my monitor to 100% brightness. I was getting pummeled by asteroids before Hammond says, "Give me another minute." (or something like that - the first time he says anything). I turned the brightness up and it made an immediate impact as I was getting to the last comment he says before the AI takes over. This will help you more in the beginning than it will later on as it allows you to pick off many asteroids before things get hectic.
-Try to keep your turret below the middle of the screen. As you know, the turret blocks your view if you're chasing asteroids that are going to hit above you.
-Don't chase asteroids you're likely not going to hit. If an asteroid is flying fast and it's already near the top or side of your screen, don't bother trying to get it unless it's a big one OR if you see there will be a slight break in the upcoming action. Chasing lost causes leaves openings for other asteroids to make it through and damage your shields.
-Lead your shots. The asteroids are coming toward you so place your targeting laser slightly in front of the incoming asteroid and fire off a burst.
-Smaller asteroids: Use one gun to pick off the smaller asteroids and try to keep your firing to bursts, not continuous firing because your turret will overheat. Just move your targeting laser towards the asteroid you wish to shoot and then fire. After a few tries, you'll be sniping asteroids leaving your turrets nice and cool for double turret bursts on the larger asteroids. I used the left gun for asteroids on the left side of the screen and right gun for the asteroids on the right side of the screen.
-Large asteroids: Use one gun if they're a decent distance away and then use both guns at the same time once it breaks apart. If it's close then by all means use both. Rotate your right stick in a small, tight circle when using both guns to ensure you get the asteroid fragments after the large asteroid breaks.
-Use both guns on clusters of asteroids be it a cluster of smaller asteroids or a large asteroid that has fragmented.
-Just try to get through this section the first couple of times you play it, don't quit after you get below 50%. This will give you a reference of how much time you have after Hammond says something. Then, once you're comfortable with how long you have to defend the USG Ishimura, just /quit the game and start over once your shields get below 50%.
-Take the advice of the name of this achievement. Seriously. I was at 83% when Hammond says his last comment and ended up below 50% because I thought I had it in the bag... took me another 10 minutes to get the achievement.
P.S. I was just kidding about the cat too.
EDIT: Here's a great tip by sloeJAKE:
"I kept a game save and came back after I had all the other achievements"
Try to remember not to save over the file! This will allow you comeback at different times and give it a shot again and, more importantly, allow you to continue progressing the story of Dead Space at your leisure. Good luck!