Hi BulletCurtain,
I just flew out of that very same asteroid belt seconds ago. It's simple, only when you get used to it. But it can be insane - just as the pilot says - dependng on your play rank and the difficulty.
Use the Thor's Scatter shot. Try to place your shots so that they split up when they hit the asteroids in front of you. This will guarantee that they break apart and the debris chunks will fly into areas that are out of your way.
Pick a route - don't try to destroy them all or as many as you can. You
will take damage doing that. There is a predetermined route that makes it easy, consisting of smaller rocks that won't split up. Try to look for it. Unless you're going for a high score run, resist the urge to blast your way through to the multiple score-related extras you see surrounded by larger asteroids.
Mexxus II's Magma hardpoint works well also, but it tends to cause other asteroids to break apart and throw unnecessary debris in your way.
Warning: Spoiler!Finally, the best fighter for this particular spot is Prototype X. Its Beam hardpoint does exactly what it did best in Himmelssturmer's Outer Rim (world 4) asteroid belt, only better. You can't go wrong with it in this particular area.
If you have a limit attack ready, or a shockwave, you might also consider using it here if you're in a tight spot, but I recommend saving both for the enemies that appear just after you emerge from the asteroid cluster (when Ellen says, "There's a whole squadron accompanying the mothership!") - this is where play ranks tend to simply die.
Lastly, you may be tempted to grab the Chain Rings that cluster to the far right of the screen. Grabbing these is risky and unless you move just right, you'll get hit.
Good luck!
Hope this helps!