Defeat The Masked Man, The Man in White Clothes, and 8 tough enemies in a row. Your health restores by 25% each round.
It's pretty easy to take out the first 2 guys with the pistol fighting style (spam the square attack). The fight with the 8 guys is another story... The guy with the hammer has not come here to mess around - if he hits you he WILL fuck you up. He does some serious damage, so stay well clear of him. Using the heat gauge you built up from the first 2 rounds, use the Wild Dance "Crowd Dispersion" heat attack as much as you can. Focus on taking out all enemies except the guy with the hammer (using heat actions and square attacks) but watch out for the hammer guy! After taking out everyone else, use the pistol style to take out the hammer guy from distance (but for the love of god, dodge roll backwards if he gets too close or starts attacking).
Defeat the Komuso, Thomas Glover, and 10 British Soldiers plus a Bear in a row. Your health restores by 25% each round.
Defeating the Komuso and Thomas Glover is, again, pretty simple with the pistol. But... Holy fucking shit, if you are not prepared for the final fight you WILL get your ass handed to you almost instantly. AS SOON as the final fight starts, switch to Wild Dance and go over to a group of British soldiers and use the Crowd Dispersion heat action, like in the first challenge. Do this again to the other group and most of them should be taken out (you really do have to act fast though, you cannot fuck around admiring your work after taking out the first group). Finish any remaining soldiers with the square attacks (but watch out for that bear!). Take out the bear from distance with the pistol style.
Defeat Takeda, Harada, and Ito in a row. Your health restores by 25% each round.
Compared to the first 2 challenges, this is extremely easy. They can all be taken down pretty easily with the pistol fighting style (square spam).
Defeat Okita, Nagakura and Kondo in a row. Your health restores by 25% each round.
Again, like the previous challenge, easy compared to the first 2, but more difficult than the 3rd challenge (because the bosses themselves are tougher). Can all be taken out fairly easily with the pistol style.
Defeat Yoshida, Tokugawa, Okada, Katsura, Saigo, Akimoto, Sasaki, and Takechi in a row.
Unlike the previous challenges, your health does not restore after each fight.
You are forced to use hand-to-hand style against Saigo, but for everyone else just use the pistol style (got to love how broken that style is when you spam square). Be as careful as you can to avoid taking damage. There is no time limit, so there's no need to rush.
If you want to use heat actions, be careful, because some of the bosses have a quick-time event before you can pull off the heat action and if you fail it you will take a lot of damage.
The first fight is simple - use the pistol square attack and keep your distance - watch out for his swings.
In the second fight, watch out for the 2nd phase of the battle, because he starts throwing shit at you, which will lose you some health.
The Okada fight is another case of spamming square and keeping your distance.
Same again with Katsura, but be careful because the room is quite small.
The Saigo fight takes a while, but be as careful as you can and you won't lose much (if any) health - dodge his attacks and throw a few square attacks to chip away at his health.
The Akimoto fight is easy, even though the room is small. Just barrage him with square attacks and stay away from him.
Sasaki is another case of spamming square and keeping your distance.
For the final fight, Takechi, I certainly hope you saved as much health as possible. The first phase is easy - just spam square pistol attacks as usual. In the second phase it's very difficult to avoid taking damage, since he uses the Wild Dance style and will shoot at you with his pistol. The final phase shouldn't be much trouble - keep spamming square.