What important attributes must a good HR staff posses? How do you handle difficult situations among employees/clients?

First, to know more of each employees characteristic,  from here you will know how and what kind of approach you are going to use. 

A client is always the important part of the business. be clear about what you can offer to them avoid mentioning an impossible service you cant do. 

both require a thorough explanation to reach their understanding.

interactive, firm decision maker