Array
(
    [38] => Array
        (
            [name] => Categoria Raiz 1
            [link] => https://...
            [id_parent] => 0
        )

    [205] => Array
        (
            [name] => Subcategoria 1
            [link] => https://...
            [id_parent] => 38
        )

    [206] => Array
        (
            [name] => Subcategoria 2
            [link] => https://...
            [id_parent] => 38
        )
    [484] => Array
        (
            [name] => Categoria Raiz 2
            [link] => https://...
            [id_parent] => 0
        )
    [485] => Array
        (
            [name] => Subcategoria 3
            [link] => https://...
            [id_parent] => 484
        )

    [39] => Array
        (
            [name] => categoria Raiz 3
            [link] => https://...
            [id_parent] => 0
        )

    [147] => Array
        (
            [name] => Subcategoria 4
            [link] => https://...
            [id_parent] => 39
        )
)

<?php
foreach($array as $key => $value) { ?>
    <li data-id_parent="<?php echo $value['id_parent']; ?>">
        <a href="<?php echo $value['link']; ?>"><?php echo $value['name']; ?></a>

    <?php
            if (!isset($id_anterior)) { ?>
                <ul>
    <?php   } else {
                if ($id_anterior != $value['id_parent']) { ?>
                    </ul>
                    <ul>
    <?php       }
            }
    ?>
    </li>
    <?php

    $id_anterior = $key;
}
?>

<li data-id_parent="0">
    <a href="https://...">Categoria Raiz 1</a>
    <ul>
        <li data-id_parent="38">
            <a href="https://...">Subcategoria 1</a>
        </li>
        <li data-id_parent="38">
            <a href="https://...">Subcategoria 2</a>
        </li>
    </ul>
</li>
<li data-id_parent="0">
    <a href="https://...">Categoria Raiz 2</a>
    <ul>
        <li data-id_parent="484">
            <a href="https://...">Subcategoria 3</a>
        </li>
    </ul>
</li>
<li data-id_parent="0">
    <a href="https://...">Categoria Raiz 3</a>
    <ul>
        <li data-id_parent="39">
            <a href="https://...">Subcategoria 4</a>
        </li>
    </ul>
</li>

$menu = [
    38 => [
            'name' => 'Categoria Raiz 1',
            'link' => 'https://...',
            'id_parent' => 0
    ],
    205 => [
            'name' => 'Subcategoria 1',
            'link' => 'https://...',
            'id_parent' => 38
    ],
    206 => [
            'name' => 'Subcategoria 2',
            'link' => 'https://...',
            'id_parent' => 38
    ],
    484 => [
            'name' => 'Categoria Raiz 2',
            'link' => 'https://...',
            'id_parent' => 0
    ],
    485 => [
            'name' => 'Subcategoria 3',
            'link' => 'https://...',
            'id_parent' => 484
    ],
    39 => [
            'name' => 'Categoria Raiz 3',
            'link' => 'https://...',
            'id_parent' => 0
    ],
    147 => [
            'name' => 'Subcategoria 4',
            'link' => 'https://...',
            'id_parent' => 39
    ]
];

$organized = [];

foreach ($menu as $index => $item) {
    if (isset($organized[$item['id_parent']])) {
        $organized[$item['id_parent']]['child'][$index] = $item;
    } else {
        $item['child'] = [];
        $organized[$index] = $item;
    }
}

array(3) {
  [38]=>
  array(4) {
    ["name"]=>
    string(16) "Categoria Raiz 1"
    ["link"]=>
    string(11) "https://..."
    ["id_parent"]=>
    int(0)
    ["child"]=>
    array(2) {
      [205]=>
      array(3) {
        ["name"]=>
        string(14) "Subcategoria 1"
        ["link"]=>
        string(11) "https://..."
        ["id_parent"]=>
        int(38)
      }
      [206]=>
      array(3) {
        ["name"]=>
        string(14) "Subcategoria 2"
        ["link"]=>
        string(11) "https://..."
        ["id_parent"]=>
        int(38)
      }
    }
  }
  [484]=>
  array(4) {
    ["name"]=>
    string(16) "Categoria Raiz 2"
    ["link"]=>
    string(11) "https://..."
    ["id_parent"]=>
    int(0)
    ["child"]=>
    array(1) {
      [485]=>
      array(3) {
        ["name"]=>
        string(14) "Subcategoria 3"
        ["link"]=>
        string(11) "https://..."
        ["id_parent"]=>
        int(484)
      }
    }
  }
  [39]=>
  array(4) {
    ["name"]=>
    string(16) "Categoria Raiz 3"
    ["link"]=>
    string(11) "https://..."
    ["id_parent"]=>
    int(0)
    ["child"]=>
    array(1) {
      [147]=>
      array(3) {
        ["name"]=>
        string(14) "Subcategoria 4"
        ["link"]=>
        string(11) "https://..."
        ["id_parent"]=>
        int(39)
      }
    }
  }
}

function echoList($array) {
    echo '<ul>';

    foreach($array as $item) {
        echo '<li data-id_parent="'.$item['id_parent'].'"><a href="'.$item['link'].'">'.$item['name'].'</a>';

        if (isset($item['child']) && !empty($item['child'])) {
            echoList($item['child']);
        }

        echo '</li>';
    }

    echo '</ul>';
}

echoList($organized);

<ul>
    <li data-id_parent="0">
        <a href="https://...">Categoria Raiz 1</a>
        <ul>
            <li data-id_parent="38"><a href="https://...">Subcategoria 1</a></li>
            <li data-id_parent="38"><a href="https://...">Subcategoria 2</a></li>
        </ul>
    </li>
    <li data-id_parent="0">
        <a href="https://...">Categoria Raiz 2</a>
        <ul>
            <li data-id_parent="484"><a href="https://...">Subcategoria 3</a></li>
        </ul>
    </li>
    <li data-id_parent="0">
        <a href="https://...">Categoria Raiz 3</a>
        <ul>
            <li data-id_parent="39"><a href="https://...">Subcategoria 4</a></li>
        </ul>
    </li>
</ul>