how to bold part of the post title

Try creating a child theme first. Copy slider.php to your child theme and change this:

<h2 class="entry-title"><a href="<?php the_permalink(); ?>" title="<?php the_title_attribute(); ?>" rel="bookmark"><?php the_title(); ?></a></h2>

to this:

<?php
$title = get_the_title( $post->ID );
$new_title = '';
// get title before ":";
$before = substr( $title, 0, strpos( $title, ':' ) );
if ( $before ) {
	$new_title .= '<strong>' . $before . '</strong>' . stristr( $title, ':' );
}
$title = ( '' != $new_title ) ? $new_title : $title;
?>
<h2 class="entry-title"><a href="<?php the_permalink(); ?>" title="<?php the_title_attribute(); ?>" rel="bookmark"><?php echo $title; ?></a></h2>

it doesnt help, doing what you said makes the whole of the slider title bold and worse messes with the drop down menu, instead of dropping down all menu items become a part of the menu tabs and the top alignment gets messed up as well..

see link below for better understanding

https://www.riseleadershipgroup.com/wptest19_2/

and it also undoes the changes like background image

totally alternative approach:

add this filter to functions.php of your theme or child theme:

add_filter( 'the_title', 'bold_before_colon' );
function bold_before_colon( $title ) {
if( is_sticky() && strpos( $title, ':' ) ) $title = '<span>'.preg_replace('#(:)#',':</span>',$title,1);
return $title;
}

add this line to style.css of your theme or child theme:

#slider .entry-title span { font-weight: bold; }

didnt work, I added the filter to functions.php on the first line and added the css code but the whole title becomes bold instead of just the part before colon ??

I see it working in the web page you have linked earlier; IE8 and FF20

try to clear the browser cache, with ‘CTRL F5’ or (several) ‘reload’

omg! thankyou sooo very much Mr. alchymyth! it is working, thanks alot i could not have figured it out myself! really thanks a bunch