This module responsifies vertical tabs in admin pages. You will have Drupal 8 like vertical tabs with only enabling it:

For desktop resolutions vertical tabs will appear in a right sidebar. However, you can also choose vertical tabs to appear on left sidebar through module's administration page.
For mobile resolutions vertical tabs will appear at the bottom of the page.

You can choose following options on module's administration form:

Append show/hide button to vertical tabs top. This allows users to dynamically hide and show vertical tabs.
Collapse all vertical tabs by default.
Which side the vertical tabs will be on wider screens.
Width of content and vertical tabs (in percentage).
Width which sets the breakpoint between mobile and desktop versions of vertical tabs.
You can specify a blacklist of paths where this module should be disabled.
Restrict responsified vertical tabs per role.
Option to enable module on frontend
Whitelist to force vertical tabs to be responsive

It has been tested with these administration themes:

Integration with Field group module

This module is compatible with add/edit node forms that use "Fieldsets", "Horizontal tabs" and "Vertical tabs" created with Field Group module. Notice if you create your custom vertical tabs for a content type with Field group, Vertical Tabs Responsive will render all your custom vertical tabs together with drupal's standart vertical tabs!

Whitelisting & Blacklisting

This module tries to detect automatically forms where vertical tabs could be responsified with no side effects. If you have a form where vertical tabs are not responsified you could try whitelisting it. On the other hand, blacklisting is useful when this module automatically responsifies vertical tabs of a form you wouldn't want to be responsified.

Common blacklist paths:

admin/content/file*
admin/config/regional*
admin/structure/menu-position*
admin/config/development/jquery_update
admin/config/content/formats*
admin/config/content/ckeditor*
admin/config/content/biblio*
admin/config/media/flexslider*

Known issues

Don't use this module together with Role Theme Switcher module (won't fix).
Don't use this module together with Node form columns module because it may break a bit the style of node form pages (won't fix).

Similar modules

Responsive Vertical Tabs (sandbox): This module does the same as mine except that it doesn't allow configuration of content & vertical tabs width. However, this module is not compatible with fieldsets and horizontal tab groups. I tried to fix his code but finally I found it much easier to to do it from scratch. Some of this module's code is based on this module.
Node form columns: This module doesn't responsify vertical tabs but it allows you to put fields (including vertical tabs) on the right side or in the footer of node form pages.

Recommended modules

Vertical Tabs Config: This module allows you to decide vertical tabs order and to hide vertical tabs on add/edit node pages depending on content type and role.

IMPORTANT: If you find any bug, please let me know. Thank you!

Vertical Tabs Responsive

Issues