Translation Plugin

You can not translate within the Adobe Reader but you can open the PDF file in the browser and add some translate extension in it and you can instantly translate within the browser to any language. Thanks 

Adobe Reader wouldn't be the proper tool to translate a file anyway since, to put it simply, it lacks all the editing features that you normally need to translate a document from one language to another.

You would want to work on the original file instead (Word file or InDesign file for instance) so you can also change the font if needed, handle hyphenation correctly, etc.

Also, translators, even if they're not professionals, may want to access tools that would speed up their work, such as translation memories.

So, the best way to translate a PDF is translating the source file using a translation tool.

If you're working with InDesign files, you might want to check out Redokun (disclaimer: I'm a co-founder), otherwise, there are plenty of translation tools that work with pretty much every file format.

There is a tool doing what you ask. Its name is QTranslate. Greetings!

I've never heard of such a plugin, and I doubt it will be feasible to implement one.

I can think of a possible way of doing it with a script, but it would still require supplying it with a complete dictionary for the translations.

Edit: I was thinking about this question, and actually it is possible to achieve something similar to this using a script (in Acrobat).

In fact, in the past I've developed a script that does just that, pretty much. You just need to feed it with the bi-lingual dictionary...