Try using .* since they're arrays.
'tutorial_titles.*' => 'string|required_with:tutorial_links',
'tutorial_descriptions.*' => 'string|required_with:tutorial_links',
https://laravel.com/docs/5.6/validation#validating-arrays
As far as looping, it's just like a normal array.
$titles = $request->tutorial_titles;
$descriptions = $request->tutorial_descriptions;
foreach ($titles as $key => $title) {
echo $title;
echo $descriptions[$key];
}
That assumes there is 1 title for each description and the arrays are present...
And for saving them to the related model: https://laravel.com/docs/5.6/eloquent-relationships#inserting-and-updating-related-models