Woocommerce Checkout form validation inside payment plugin

Solution:

add_action('woocommerce_checkout_process', 'my_validation');

function is_phone() { 
    $some_field = $_POST['your_field_name']; //this is how you get the value of your field.
    if($some_field == "") { //here we check if the field is empty, you can add your rules.
        wc_add_notice( __( 'Your field is empty, please fill it' ), 'error' );
    }
}

And at the end we add a notice with the message you want to show, also we note it is an error. This goes into functions.php of your theme. You can edit the message you get and also the rule. Let me know if this helps.