Personally, I have only tried one hair mineral analysis lab called "Doctor's Data" but I believe it to be the most accurate. This opinion comes after speaking to doctor's and others who are familiar with the handful of labs that do hair mineral testing. It is more expensive, but money will buy the quality you need to get your health back on track (after all, an accurate test will save you from spending money on supplements you don't need).
If I could just say a few things about the test itself:
It is very important to conduct the test as strictly as possible. Do not wash your hair beforehand (as long as possible). A day or two would be fine. Take the hair from the back of the head and only add the centimetre of hair that is closest to the scalp (discard the rest - it will screw up the test)/
Besides that, using natural shampoos or less harsh shampoos for a few weeks before the test will help return a more accurate result. Dying or treating hair will also screw up the test, so try to refrain from that. A think Doctor's Data has a website - a google search should reveal this.