Try to use the lowest tolerance model that your printer can handle. On the tightest model you may have to pry at the pieces after printing, but the work is very much worth it for the tighter fit. If you can't get the outer pieces to detach from the outer square you can try inserting a thin knife between the piece and the outer portion to break them apart.

I recommend lubing the puzzle after printing to increase the smoothness of the motion.

If possible: Change the filament color for the upper three layers. (Two layers for the 0.2mm tolerance version)