Warriors Orochi

In Shu, you have to safely escort all of the peasants to the escape point; all three units marked "Peasant" must survive and must reach the escape point. Additionally, you must defeat Lu Bu (although, since he appears in your path, it's difficult to get past him without defeating him.

As for the others, I'm not so sure.

Wu story - Beat Honda at the altar, then beat him quickly again when he shows up for an encore after a few minutes. He appears at the upper-right most area on the map the second time, so prepare yourself by getting to that area as quickly as possible. Then just finish the rest of the stage normally, and once you beat Dong Zhuo, you'll get the message stating that Honda was impressed by your awesome power.