Retained Search means that you must pay something up front to have the Headhunter start to search – if you are not willing to do so you should maybe reconsider.
If you pay peanuts you get monkeys.
If a recruiting company is willing to work for you on a contingency (no up front payment) basis you are not dealing with a top player in the market. It is your free choice; just know who you are dealing with. If you are not sure the recruiter will be successful in the search, and therefore you don’t want to pay up front, look further until you find someone that you believe will deliver (check references). Otherwise you may end up wasting both your own time and having to deal with a vacancy for a longer period – that is expensive – not an up front payment.