You can use robots.txt to do so. To stop certain category to be indexed by search engine you can use below code in your robots.txt file
User-agent: *
Disallow: http://mysite.com/category_2/sub-category_2.html
You can add the links of whichever category you want in similar fashion. Hope you are clear on this.
To learn more about robots.txt you can refer some links robots.txt, robots.txt tutorial, robots.txt in Magento
To add robots.txt you just need to create a file named robots.txt and upload it on the root of the folder so it is accessible like www.mysite.com/robots.txt
After that you can write the above code in that file and upload it in your root folder