When you have bought all of the characters, and unlocked the 5 bonus characters, go to the Museum option in the Main Menu, select Chain of Souls and the achievement is unlocked.
Bonus Characters: (Complete Stage 3 of Story Mode with Certain characters to encounter one of these)
Shura (Ivy, Taki, Raphale, Setsuka, Seon Mi-Na, Cervantes, Kamikirimusi)
Ashlotte (Astaroth, Maxi, Lizardman, Sophitia, Rock, Talim, Angol Fear)
Kamikirimusi (Xianghua, Tira, Cassandra, Mitsurugi, Amy, Yun-Seong, Shura)
Angol Fear (Kilik, Algol, Zasalamel, The Apprentice, Scheherazade)
Scheherazade (Voldo, Hilde, Nightmare, Siegfried, Yoshimitsu, Yoda, Ashlotte)