Since this problem seems has been already asked several times and there is still no good answer for that, I'd like to try to provide my solution from the template override side. The steps are quite complex but it should be easy.
Note : I'm using Joomla 3.4.4 and template protostar while creating this tutorial
First, copy this files :
[root]/components/com_tags/views/tag/tmpl/default.php
[root]/components/com_tags/views/tag/tmpl/default.xml
[root]/components/com_tags/views/tag/tmpl/default_items.php
to
[root]/templates/your_template_name/html/com_tags/tag/default.php
[root]/templates/your_template_name/html/com_tags/tag/default.xml
[root]/templates/your_template_name/html/com_tags/tag/default_items.php
replace the file names to something you like, for example 'taggedblog', so it will become :
[root]/templates/your_template_name/html/com_tags/tag/taggedblog.php
[root]/templates/your_template_name/html/com_tags/tag/taggedblog.xml
[root]/templates/your_template_name/html/com_tags/tag/taggedblog_items.php
Open the file [root]/templates/your_template_name/html/com_tags/tag/taggedblog.xml at the top of file you will see this code :
<layout title="com_tags_tag_view_default_title" option="com_tags_tag_view_default_option">
change that to
<layout title="Tagged Blog" option="taggedblog">
At this point, you should see a new menu item type called Tagged Blog when creating a new menu item from your menu manager. See this image below
Now, Open file [root]/templates/your_template_name/html/com_tags/tag/taggedblog_items.php
at lines 62 delete this code :
<ul class="category list-striped">
and it's </ul>
closing tag at lines 90
then, still on the same file, delete these codes started at lines 64:
<?php if ($item->core_state == 0) : ?>
<li class="system-unpublished cat-list-row<?php echo $i % 2; ?>">
<?php else: ?>
<li class="cat-list-row<?php echo $i % 2; ?> clearfix" >
<?php endif; ?>
at lines 70, and closing tag </li>
at lines 85
Next, add <div class="span5">
at 64 lines after the code <?php foreach ($items as $i => $item) : ?>
and add closing </div>
before the <?php endforeach; ?>
Next, arround lines 77 before the code <?php if ($this->params->get('tag_list_show_item_description', 1)) : ?>
add this code :
<?php
$db = JFactory::getDBO();
$query = $db->getQuery(true);
$query->select('introtext')->from('#__content')->where('id=' . (int)$item->content_item_id);
$db->setQuery($query);
//displaying the intro image
$images = json_decode($item->core_images);
if(!empty($images->image_intro)) {
echo '<img src="'.$images->image_intro.'">';
}
//displaying the intro text
$introtext = $db->loadResult();
echo $introtext;
?>
At this point, introtext and intro image should have been displayed on the the website.
Now, open the file [root]/templates/your_template_name/html/com_tags/tag/taggedblog.php , around lines 51 you will see this code <?php echo $this->loadTemplate('items'); ?>
, change that line to :
<div class="row"><?php echo $this->loadTemplate('items'); ?></div>
That's all.
Now try to create a menu item with Tagged Blog type from your joomla menu manager, and see the result.
To make things easier, I have uploaded those files above in here. Have fun!