This is a purely tactical scenario. It's pretty easy, as long as you're an AoE tactical expert, because you get way more troops than you need. Of course, if you cheat, it becomes a lot easier.
Explore your starting position with a horse archer. You can't go very far, because you are surrounded by enemy archers, and they can see almost as far as you. Withdraw and organize your troops. You want 2 Cavalry groups, and one group for each of your other unit types. You will not need the infantry at all. One of your Cavalry groups will also not be needed, and the foot archers can only be used in certain situations.
For most of this scenario, the most important principle is damage avoidance, because you have no way of healing any damage. You can hope to find a priest somewhere, but that's only a hope at present. The main way of avoiding damage is to avoid combat. Unfortunately, that simply is not going to work. You will be forced to fight every single enemy unit and Tower, except those that aren't a threat, and you may as well fight those, too.
The primary damage avoidance procedure if you have to fight is the Ambush tactic. In AoE, AI units target archers whenever they can, and generally the weakest unit in a group. If you can properly place your melee units in front of your missile troops, you can get a lot of free hits. Another important tactic is to take evasive action with units that are being attacked while their friends stand and shoot.
Because you are surrounded by enemy archers, you will have to fight your way through the encirclement. As soon as you engage the first Shikoku unit, a lot of Shikoku troops start heading in your direction, and not just the ones that are in sight range of the combat. About 10 of these troops will get eaten by lions. You will kill about 20 Shikoku units very close to your starting position.
When you have cleared a reasonable space around your starting position, and no more Shikoku units seem to be arriving, start exploring the rest of the map with your horse archer group. Push forward as far as you can in all directions, looking for weak spots, and destroying anything that can easily be destroyed. Call for reinforcements as appropriate. Eventually, you are forced through a choke point on the NE map edge. Then you have to swing around and clear out the rest of the continent. You find no help at all anywhere on this continent. In all of this, any of your archers can attack any of the Shikoku Towers with impunity, but stay alert for counter-attacks!
When the continent is clear, cut your way through the wall in the very west. You then recruit some Transports, and, on the victory island, a bunch of troops. These troops are of lower quality than what you already have, so you won't need them. You didn't actually lose any units, did you? The catapults, however, are important, and the priests are especially important, because your horse archers will be pretty battered by now.
At this point, you can win any way you like. You strongly outnumber the Shikoku forces by now, you have much higher mobility, your best troops are of better quality than theirs, you can heal your units, and you can convert their units. Resistance is futile.