It's nightmare for me...
Why it so difficult???
K2 tags modules creates links to tags page like

site.com/component/k2/tag/test

Articles creates links to same tags pages like

site.com/parent_category/sub_category/tag/test
or
site.com/parent_category2/sub_category2/tag/test

I have hidden menu item to main parent category and my mind, that all links to tags pages must looks like

site.com/menuitem/alias/tag/test - for all tag link (it must be same).

What's going on?

In order for all tags to have the same URL the hidden menu item must not point to any K2 category. Just leave it blank.

Thanks. Got it.

Unfortunately, I still have problem.

I created hidden menu item and not point it to any K2 category.

Now tags module and k2 articles displays links like:

items/tag/test

and it's very good.

But on main page tags module displays links as

items/itemlist/tag/test

How I can fix it?

This part "itemlist/tag/" is the default URL.
You can change it by enabling K2' Advanced SEF.
These options are located in K2's settings.