Hi Thanh.  Thank you for your question.  Key criteria should be the headhunter's (HH) knowledge about industry, the market trends, the level of information they have on their clients, and their track record and integrity.  While all this can be subjective, you should seek a more objective view through others who have used HH's and your own due diligence.  I find that Do Chi's recommendation of a ranking system is very good one that is often used for many other professional service providers such as lawyers, doctors, dentists, travel business, etc.  Professional, qualified HH's and HH search firms would welcome this!