Perform these tasks to unlock a new character or a variation of an existing one:

Acarinaworm Amber
Finish 2 player story mode using Kamen Rider Drake without a partner

Aracneworm Flavus
Finish 2 player story mode using Aracneworm Rubor without a partner

Aracneworm Nigrita
Finish 2 player story mode using Aracneworm Flavus without a partner

Kamen Rider Caucasus
Complete the Worm story route in 1P mode

Kamen Rider Hercus
Complete the Kabuto story route in 1P mode

Kamen Rider Ketaros
Complete the Rider story route in 1P mode

Kamen Rider Kick Hopper
Finish 2 player story mode using Kamen Rider TheBee (Yaguruma) without a partner

Kamen Rider Punch Hopper
Finish 2 player story mode using Kamen Rider TheBee (Kageyama) without a partner or collect 30 Tropical Ramen in survival mode

Kamen Rider TheBee (Kagami)
Finish 2 player story mode using Aracneworm Nigrita without a partner

Kamen Rider TheBee (Kageyama)
Finish 2 player story mode using Kamen Rider Kabuto on "High" difficulty without a partner

Scorpioworm
Finish 2 player story mode using Kamen Rider Sasword without a partner

Tarantesworm Purpura
Finish 2 player story mode using Kamen Rider Gatack without a partner

Ucaworm
Complete 2 player survival mode (100%) with 5 different characters or collect 50 Tropical Ramen in Survival mode

Verberworm Rota
Finish 2 player story mode using Verberworm without a partner

ZECT Trooper Shadow status
Finish 2 player story mode using the standard Zect Trooper on "Very Easy" without a partner