Mac wont startup in Osx

Let me start off by saying that i have a bootcamp installed on my mac, and using that partition a lot. Therefore I'm unsure when the mac partition went south, since i only boot from that partition maybe once every 2 weeks.

This is what happens when i try to boot my mac. (BTW it's a mid 2011 Imac 27" 2.4 Ghz)

Apple logo appears along with startup chime.

Then after a few seconds a progress bar appears which then loads up fully after about 10 minutes. After the progress bar finishes it disappears. Then after a few seconds the mac shuts down. When i reboot it does the same thing again. All through the load of the bar the mac makes sounds reminiscent of it shutting off.

I've tried booting in recovery and repairing with disk utility, but it gives me the statement that it cannot repair the HDD and i should back up all files immediately. I've seen forums on the web where people talk about prompting the mac to try again and then being successful after a few attempts and i have tried that but even after it has started repairing seeming to work, it ends up saying that it cannot repair the partition.

All the while i can still boot into my windows partition with no problems.

If you tech savvy people have no idea what i can do to save the mac partition, i would like to hear if any of you have any idea how i can backup some of the files from the mac partition through my windows partition? 🙂

Thanks in advance

Lakkermoose