From SNT-TC-1A 2006
6.3.2 NDT LVL III
6.3.2.1 Have Graduated from a minimum of 4 year college / university with a degree in engineering of science, plus one additional year of experience beyond the level II requirements in NDT in an assignment comparable to to that of an NDT LVL II in the applicable NDT method….or

6.3.2.2 Have completed with passing grades at least 2 years of engineering or science study at a university, college, or tech school plus 2 additional years beyond the level II requirements in NDT in an assignment at least comparable to that of NDT LVLII  in the applicable method ….or
6.3.2.3 Have four years experience beyond the LVL II requirements in NDT in an assignment  at least comparable to that of an NDT LVL II in the applicable method
The above requirements may be partially replaced by experience as a certified NDT LVL II or by assignments at least comparable to NDT LVL II as defined in the employer’s written practice.

My advice to you is get a copy of the recommended practice as a LVL III you will be required to know the answer to the very question you have asked.
You will need to take the NDT LVL III basic and then take the LVL III in the desired method.
The basic test is only taken once but each method you seek will be tested on.
Currently I am studying for my LVL III in MT so if any1 has any more advise or a correction to my post please let us Know.
Be Well Informed about all NDT methods,and the recomended Practice SNT-TC-1a
Hope this helps

MDK