I did similar thing recently. Here is my suggestion:
1. calculate distance between every pair of X. The distance can be equal to 1 - absolute value (correlation), or a kind of distance for multivariate variables
2. based on the distance matrix, clustering X variables. For instance, draw a tree to illustrate the association.
3. you may see several clusters from the tree. pick only 1 variable from each cluster will meet the objective.
Alternatively, you may consider factor analysis or principal component analysis to see whether some functions of X variables can represent all X variables or some X variables can explain majority variation.