You could do this by applying multiple client validations. The first would be a required type of validation on the first text field. Next you would add in a conditional validation response. For the conditional validation you would set the triggering form element to the first text field and the target to the second. You would then specify if the trigger is valid, do not validate the target.
You would repeat this set of a required and conditional validation but for the second and third elements rather than the first and second. After you have all of the required and conditional validations in place you can then apply all of the regular validations to the form including the required validations for these fields. The validations on these fields will only be triggered if the triggering validation fails.
