Ok, I figured it out, and yes it was a bone-head mistake. The “id” needed to be changed on the trigger to just “id” without anything before it and the target “id” needed to be changed from an underscore to a dash and that did the trick.
Here is the revised code that works:
add_action( 'genesis_entry_content', 'awards_achievements_content', 11 );
function awards_achievements_content() {
if ( is_single() && genesis_get_custom_field('awards_achievements') )
$col_id = 'awards-achievements';
echo '<div class="collapseomatic" id="' . $col_id.' " title="Awards & Achievements">Awards & Achievements</div>';
echo '<div id="target-' . $col_id . '" class="collapseomatic_content">' . genesis_get_custom_field('awards_achievements') . '</div>';
}