This must be done in Story mode.

Character	How to unlock
Hojo Ujimasa	Beat story mode with 5 different characters.
Kasuga	Beat story mode using Sarutobi Sasuke or Tachibana Muneshige.
Maeda Toshiie	Beat story mode using Hisahide Matsunaga or Tenkai.
Matsu	Beat story mode using Mogami Yoshiaki or Otomo Sorin.
Takeda Shingen	Beat story mode with 8 different characters.
Uesugi Kenshin	Beat story mode using Katakura Kojuro or Kobayakawa Hideaki.