Upon further investigation, it looks like this K2 Specific extension is best option to resolve Duplicate Content issue:

Website:
www.managecms.com/extensions/k2-canonical-links

Description:

With Canonical Links for K2 ranked in Top 5 K2 extensions you will get true canonical links for your K2 articles. We have tried other solutions offered on the market, tried Joomla 3 native solution, and found out that they all had issues, as reported on various forums around the web. We applied our 5+ years of experience with Joomla and K2 and developed a new plugin to solve canonical problem once and for all.

If you can reach the same K2 article with links like:

www.example.com/article
www.example.com/category/article
www.example.com/tag1/article
www.example.com/tag2/article

All of them will have the same canonical link! Not only that, but you can choose to automatically redirect users to your canonical page.

Tags and categories are fully supported. We also set canonicals for paginated series, so that Google can index properly your categories with more than one page.

Plugin is carefully tweaked so that the most appropriate link is chosen, based on your menu structure!

Thanks for the tip Joe Campbell! To use a paid extension for 29 euros, I think it's absurd! Some of these extensions of the working tool for this problem? Previously used Artio JoomSEF, however, refused it, no it sense! And apparently after you turn off Atrio JoomSEF got these links...

@GermanLevi The K2 version is only 19 Euros.

I believe in paying for extensions, even if the developer provides them for free. As nothing in life is FREE.

Since, I am not a developer, I must rely others with coding abilities. Paying or giving a donation is how I show my appreciation.

Note: #JFeedback, positive rating and sharing via social media are other great ways to Give Back :)

Plugins of this kind is "crutches". The engine and components must not be problems with indexing. Otherwise the meaning of their use?! If every mistake to close the plugin or the module, the site will become too slow. So we are looking for a solution and gradually phasing out the plugins. I think back to install Artio JoomSEF, although it is also all not so simple as it turned out, he had no paid add-on refuses to work correctly with k2 users! Thanks again for the tip!

In fact you can write a function in the K2 template, which will insert these links in the tag rel=canonical! Parse the query string and from string to insert tag or rel=canonical or not!

The question still is where Google takes such a wrong image links site.com/item-name when the correct url of the website looks like site.com/category/category/item-name? Who ever knew whence their beret a search engine?

Currently, I am rendering the canonical tag by way of K2 absolute URL or an extra field override, but the real issue is the generation of bad page URLs.

This extension seems to remedy this issue.

The links could be generated from your menu structure.
A change in the menu means that new URLs where generated. A change in K2's Advanced SEF will also have similar effects.

Furthermore sitemap generating extensions can cause this issue as well.
Finally a K2 module which produces wrong URLs (Eg: does not follow the component's settings) could also be the culprit. A canonical tag will cure this headache.

I emailed extension developer (Marko) who promptly responded. After answering a few questions, I purchased the extension.

Within 2 parameter clicks my K2 URL problem is over - I am SUPER HAPPY!!!

Best of all, I have not noticed an impact on my site performance.

K2 Canonical Links receives my stamp of approval
www.managecms.com/extensions/k2-canonical-links

Nothing of the above I do not! The module I'm not using. Site map does not contain errors.