I will do my best to help you trough this but it will be up to you to implement it.
You will start by adding your checkbox to the form where you would like it to be, make sure to set the value of this checkbox. You will then need to wrap the second part of the form in a div. Next you would need to apply a client validation to this checkbox. The validation will be a required type of validation.
This is the setup for triggering the show/hide layer validation response. So next you will apply the show/hide validation response just after this required validation. For the trigger select the checkbox, then select 'if trigger is valid', meaning the box is checked, show the div that the other half of the form is in.
After this you would select the form and apply all of your regular validations.