Hi Marguerite,
Are you using the featured post slider or featured image slider. To use target_blank you need code customization inside attitude-pro -> library -> structure -> header-extensions.php
If you are using featured post slider then on line no 537 remove this line
$attitude_featured_post_slider .= '<figure><a href="' . get_permalink() . '" title="'.the_title('','',false).'">';
and add this
$attitude_featured_post_slider .= '<figure><a href="' . get_permalink() . '" title="'.the_title('','',false).'" target="_blank">';
if you are using featured image slider then on line no 598 remove this line
$attitude_featured_image_slider .= '<figure><a href="' . esc_url( $redirect_link ) .'" title="' . esc_attr( $title ) . '" >';
and add
$attitude_featured_image_slider .= '<figure><a href="' . esc_url( $redirect_link ) .'" title="' . esc_attr( $title ) . '" target="_blank" >';
hope this may help you but we recommended not to change the code because if you change the code then while updating to our new version all the customization code will be lost. So better make a child theme and first unhook the functions and then you may edit the code will be the best solution.
Thank you!