If you want to upgrade to OS X Mountain Lion please check our recommendations:
OS X Mountain Lion is available on the App Store
Note: this article is for Parallels Desktop 7 only. If you use Parallels Desktop 5 or Parallels Desktop 6 please refer to this article: https://kb.parallels.com/114410
Make sure you use the latest Parallels Desktop 7 build 7.0.15104: https://kb.parallels.com/en/4923 . Update Parallels Desktop 7 to the latest build if a previous build is installed.
Before you upgrade
To learn what Macs are supported by OS X Mountain Lion please refer to this article: https://www.apple.com/osx/specs/
How to upgrade?Follow these instructions from Apple to upgrade to OS X Mountain Lion: https://www.apple.com/osx/how-to-upgrade/