If you can master the facts, you will have your first significant strategic advantage. Know your prey. This requires research and study. One of your goals should be to know the expert as well as she knows herself. That means more than getting the expert's self-serving curriculum vitae.
Experts are creatures of public record.
Know that record. Prior depositions and writings are the most likely source of useful information, but do not ignore the lesser known sources of information such as nonpublished reports, affidavits, articles or news pieces about the expert, academic records, and litigation involving the expert. The only way to beat an expert is to be a better expert. Besides knowing the case, you also must learn that field of specialized knowledge that the expert wants to bring to bear. By reading voraciously in the field, by consulting your experts, you will become an expert in the field.