Top Three Skills -
#1 - organization and time management skills.
#2 - a thick skin - the ability to not take the job personally and to be able to leave it at the office at the end of the day.
#3 - finally - the courage to say no when the claim does not warrant want the person wants no matter how badly you may feel about the situation they are in.
Developing your expertise is an ongoing thing - I have handled claims for 16 years and still learn something new everyday. Work your diary timely, return phone calls promptly, if you tell someone you are going to do something - do it. These simple things will make your life easier and the experience comes with each new claim - no two are ever exactly alike because no two people are alike.