it takes a little bit of hand coding to accomplish this, but it can be done using server side validation.
Use the required / not blank / selection made validation type.
for the sever variable, click the lightning bolt and select the radio group, this will add code similar to:
<?php echo((isset($_POST["RadioGroup"]))?$_POST["RadioGroup"]:"") ?>
edit that to:
<?php echo((isset($_POST["RadioGroup"]) && $_POST["RadioGroup"] == "1")?$_POST["textfield"]:"ok") ?>
this tells it to check if Radio group has a value of 1. Id so, it passes the value of textfield for validation, if not it passes the value "ok" for validation which will pass.
add a second required validation, this time use the server variable:
<?php echo((isset($_POST["RadioGroup"]) && $_POST["RadioGroup"] == "2")?$_POST["textfield2"]:"ok") ?>
this checks the radio group for the value 2, if so, it validates the textfield2 form element