What are possible approaches to deal with unseparable data even after PCA?
Is your problem unsupervised? If not, the data does not need to be "visually" separable in two dimensions, you can use classifiers in multiple dimensions to create separations for you (linear or nonlinear, just depends on the classifier).

If your problem is unsupervised try other methods for clustering data such a K-Means or tree-based clustering (i.e. hierarchical).