To unlock extra characters for Mission Mode, finish the indicated task in Story Mode..

Xion: Gain the Rookie Rank 117.

Riku: Gain the Agent Rank on Day 172.

Donald: Gain the Expert Rank on Day 255.

Goofy: Gain the Master Rank on Day 296.

King Mickey: Complete the game then purchase the Return Of The King item from the Moogle Shop.

Sora: Complete all missions (100% game completion) then purchase the Soul Of Sora item from the Moogle Shop.