Oh, man, that one IS tough. I loaned my copy to a friend and he couldn't get past that one either. Here's my advice:
The number one thing to remember is: when faced with multiple aneurysms, you're best bet is to cut them out from the surrounding tissue but do not remove them yet! Only once you have all of them ready to remove should you do so.
This is so very crucial to remember. Once you've run your stylus around the yellow dots to cut the aneurysm free it will stop swelling and leave you free to attack the others. Once that's out of the way, go back and remove, drain, pull and suture the vessels.
Avoid having to out-zoom/in-zoom. After a few tries I figured out the best location to get as many aneurysm in sight as possible -- they always form in the same spot.
Avoid letting any burst -- it's nearly impossible to control the chaos that results. Use the brown serum as necessary, and don't forget to buff up with the green if vitals start to drop.
Also, they come in "waves" so use that time to heal up with the green serum. Until you suture the final vessel at the end of the "wave" no more aneurysms will sprout. Give yourself all the extra health you'll need!
http://www.youtube.com/watch?v=9lrPlIuEJCo
This video shows some of these techniques. The player does an excellent job of keeping his zoom under control, especially for the final 5.
I hope that helps!