Determine highly correlated segments
The idea you have in mind is called "feature selection" or "attribute selection". The fact that you have a categorical dependent variable and continuous independent variables is mostly irrelevant because you're expected to use an algorithm or statistical method that is suitable for your requirements.

As for feature selection methods, there are several options:


Find the subset of features that achieves better performance (usually in cross validation)
Find the subset of features that correlates highly with the target variable and low with each other (although other criteria can be used)
Use an algorithm that includes a built-in feature selection mechanism (e.g. decision trees, hierarchical bayesian methods)


Furthermore, there are several methods aimed at obtaining a good compromise between a thorough search and a reasonable time execution (e.g. best first, steepest ascent search, etc)

This question in particular provides very good suggestions for R packages.