You must complete every fight quickly and with most of your health:

No. 13 Z rank on all fights for Chapt. 1
No. 14 Z rank on all fights for Chapt. 2
No. 15 Z rank on all fights for Chapt. 3
No. 16 Z rank on all fights for Chapt. 4
No. 17 Z rank on all fights for Chapt. 5