To do all these battles really fast, try to develop any kind of harness as soon as you start (conquer the territory that has it or start with a ruler that is occupying a territory with the ability to develop the item. This will give you a horse right from the start. If you can manage to produce Unicorn Hoofs, they will speed up your horse and you can go faster. Here are some tips (these apply mostly after your 2nd or 3rd campaign, when you have unlocked most of the tactics and Assign options).
* Go straight for the territory the Ruler is in. All his territories will be yielded to you once you defeat him.
* Use the Neutral base tactic always. The game will start with neutral bases and you just have to run with your speedy horse through them and they are yours. You can build a supply chain faster on every battle this way and you won't have to fight most of the troops.
* If you are getting attacked (Defend option), just take your horse straight to the main camp and defeat the boss or Guard Captains. The battle will end.
* When Invading, if you go straight to the main camp without building a supply chain, the ruler won't appear. You have to conquer a string of bases from your camp to the enemy's, which will have a blue color throughout. This is easier with the Neutral base tactic.
* My preference: Zhou Tai and Taishi Ci.