I've done the scenario three times now and won each time, it's a fun scenario but as it's all about war, it's just to have a better strategy than the AI, which isn't that hard when you learn the tricks.
My first game was on emperor as Korea, victory on turn 38. The key here is to make a defensive stand at a good location, on emperor it's perfectly possible to make that stand at Seoul, I would guess on higher difficulties move it back to pyongyang (spelling?) where the riverline and a few good hills makes a good place for your ranged units. The other main thing is to control the sea, with your turtle ships it should be quite easy, you get some free ones every now and then and used in pairs they beat down anything coming your way and if japan can't get troops from their mainland, you can quite easily run them down. Atleast on emperor there's no use in waiting for chinese troops, imho the AI is more likely to place them in the wrong place and block your own troops.
Next I did the scenario with Japan on immortal which was a bit harder, going all the way to a time victory at turn 100. Beijing was almost impossible to get to and when I finally got a little break around turn 90 and looked to make it, those mongols to the north decided to declare on me so I had to pull back and protect what I had. Lesson learned here is that korea is easily beaten, China far more difficult, I made the mistake to only approach Beijing from the north, I'd guess hitting in the middle first, cutting their supply chain and approaching beijing from north and south is the only option if you want to make it fairly quickly. Rule of the sea is important, you'll need to get troops from your mainland safely, unfortunately you only have triremes at your
disposal, but use three in formation with naval promo and you can beat down turtleships and caravels.
Third game with the scenario was on Diety with china. Quite an easy game considering it's Diety. Victory at turn 58, which I believe could have been quicker but I played it safe and didn't rush things. Nothing much to it but to pump out troops and use them wisely and hope that the mongols to the north stay out of it long enough. In this game I rushed 3 chu-ku-no's to the front, keeping them safe while still being able to fire at the advancing japanese. Stopping the japanese advance at pyongyang so Korea still had the 3 northern cities. There I waited for a long time, holding the defensive line with my three chu-ku-no's, a cannon and two muskets, letting the
japanese hit my wall of death, earning valuable promotions, Nothing beats a chu-ku-no with +1 range and ability to fire over obstacles. While holding the line I mass produced caravels to rule the seas and effectively cutting of the japanese supply of troops from their mainland. When I finally launched the offensive I had a force of amphibious muskets and longswords hitting the southwestern coast of korea while my main force advanced from the north, with long range ranged units it was easy to clear the path for the muskets/longswords and keeping a few knights to
pillage any wajos on the way.
In all 3 games I filled the honor branch with the initial culture policies. It really is all you need for both happiness and money, defensive buildings in all cities and garrisson as needed to keep happiness at bay and there's plenty of enemies to kill for cash each round. Also, you do want the extra XP points for getting some real killer units. The rest of the policies as you please.
I haven't done any game with the forth faction which I call the mongols as I don't remember what they're called in this scenario but I would guess it might be a bit more difficult.