Writing less unnecessary code with WordPress

Try this

function cat_loop ($key){
    $fashion_cat = array(
        'category_name' => $key,
        'posts_per_page' => 4,
        'post_type' => 'post',
        'post_status' => 'publish',
        'orderby' => 'date',
        'order' => 'DESC',
        'post__not_in' => $already_posted,
        'category__not_in' => $private_categories
    );

    // Add the loop.
}

cat_loop ('fashion');
cat_loop ('beauty');
cat_loop ('lifestyle');

put the loop in function which has variable for the category_name and repeat it.
I hope this helps