Embedding WYSIWYG Editor in Custom widget needs the declaration of the fields under a form function, this will create a WYSIWYG Editor in your widget.
You can define your parameter, what all features you want to show.
public function form( $instance ) {
$rand = rand( 0, 999 );
$ed_id = $this->get_field_id( 'wp_editor_' . $rand );
$ed_name = $this->get_field_name( 'wp_editor_' . $rand );
$content="Hello World!";
$editor_id = $ed_id;
$settings = array('media_buttons' => true,'textarea_rows' => 4,'textarea_name' => $ed_name,'teeny' => true,);
wp_editor( $content, $editor_id, $settings );