How to add media from front-end to an existing post and edit file title

First add to your for the new input field:

<form id="file-form" enctype="multipart/form-data" action="<?php echo $_SERVER['REQUEST_URI']; ?>" method="POST">
    <p id="async-upload-wrap">
        <label for="async-upload">upload</label>
        <input type="file" id="async-upload" name="async-upload"> <input type="submit" value="Upload" name="html-upload">
    </p>
    <p id="image_title">
        <label for="image_title">Image Title</label>
        <input type="text" id="image_title" name="image_title" value="">
    </p>
    <p>
        <input type="hidden" name="post_id" id="post_id" value="<?php echo $post_id ?>" />
        <?php wp_nonce_field('client-file-upload'); ?>
        <input type="hidden" name="redirect_to" value="<?php echo $_SERVER['REQUEST_URI']; ?>" />
    </p>
    <p>
        <input type="submit" value="Save all changes" name="save" style="display: none;">
    </p>
</form>

then after you save the image and get an attachment id you can update the attachment metadata:

if ($_FILES) {
    foreach ($_FILES as $file => $array) {
        $newupload = insert_attachment($file,$post_id);
        //get the meta data of the attachment 
        $meta = wp_get_attachment_metadata( $newupload);
        //set the title
        $meta['image_meta']['title'] = wp_kses($_POST['image_title']);
        //update the attachment with the new title.
        wp_update_attachment_metadata($newupload,$meta);
    }
}