How to add html attributes to the “ul” html tag with “wp_nav_menu” function?

wp_nav_menu has all the documentation written there.

You just need to put “ul” in the parameter “container”.

So your modified function call will be,

wp_nav_menu( array(
    'theme_location' => 'main-menu',
    'container => 'ul',
    'container_id' => '', // put id of ul if needed
    'menu_class' => '' // as needed
) );

For custom attributes you need to use Walker class, as you have used in your function,

wp_nav_menu( array(
    'theme_location' => 'main-menu',
    'container => 'ul',
    'container_id' => '', // put id of ul if needed
    'walker' => new MainMenu_Walker()
) );

Then write the custom walker class for you menu,

/**
 * Custom walker class.
 */
class MainMenu_Walker extends Walker_Nav_Menu {

    /**
     * Starts the list before the elements are added.
     *
     * Adds classes to the unordered list sub-menus.
     *
     * @param string $output Passed by reference. Used to append additional content.
     * @param int    $depth  Depth of menu item. Used for padding.
     * @param array  $args   An array of arguments. @see wp_nav_menu()
     */
    function start_lvl( &$output, $depth = 0, $args = array() ) {
        // Depth-dependent classes.
        $indent = ( $depth > 0  ? str_repeat( "\t", $depth ) : '' ); // code indent
        $display_depth = ( $depth + 1); // because it counts the first submenu as 0
        $classes = array(
            'sub-menu',
            ( $display_depth % 2  ? 'menu-odd' : 'menu-even' ),
            ( $display_depth >=2 ? 'sub-sub-menu' : '' ),
            'menu-depth-' . $display_depth
        );
        $class_names = implode( ' ', $classes );

        // Build HTML for output.
        $output .= "\n" . $indent . '<ul class="' . $class_names . '" data-hover="dropdown" data-animations="zoomIn zoomIn zoomIn zoomIn">' . "\n";
    }

    /**
     * Start the element output.
     *
     * Adds main/sub-classes to the list items and links.
     *
     * @param string $output Passed by reference. Used to append additional content.
     * @param object $item   Menu item data object.
     * @param int    $depth  Depth of menu item. Used for padding.
     * @param array  $args   An array of arguments. @see wp_nav_menu()
     * @param int    $id     Current item ID.
     */
    function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
        global $wp_query;
        $indent = ( $depth > 0 ? str_repeat( "\t", $depth ) : '' ); // code indent

        // Depth-dependent classes.
        $depth_classes = array(
            ( $depth == 0 ? 'main-menu-item' : 'sub-menu-item' ),
            ( $depth >=2 ? 'sub-sub-menu-item' : '' ),
            ( $depth % 2 ? 'menu-item-odd' : 'menu-item-even' ),
            'menu-item-depth-' . $depth
        );
        $depth_class_names = esc_attr( implode( ' ', $depth_classes ) );

        // Passed classes.
        $classes = empty( $item->classes ) ? array() : (array) $item->classes;
        $class_names = esc_attr( implode( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item ) ) );

        // Build HTML.
        $output .= $indent . '<li id="nav-menu-item-'. $item->ID . '" class="' . $depth_class_names . ' ' . $class_names . '">';

        // Link attributes.
        $attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
        $attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
        $attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
        $attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';
        $attributes .= ' class="menu-link ' . ( $depth > 0 ? 'sub-menu-link' : 'main-menu-link' ) . '"';

        // Build HTML output and pass through the proper filter.
        $item_output = sprintf( '%1$s<a%2$s>%3$s%4$s%5$s</a>%6$s',
            $args->before,
            $attributes,
            $args->link_before,
            apply_filters( 'the_title', $item->title, $item->ID ),
            $args->link_after,
            $args->after
        );
        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
    }
}

I have added your html attributes to the inside start_lvl function. You can debug this code and modify as you need it.

I have taken this code from WordPress Menu Custom Walker Class