Here's my strategy that worked very well last night and ended me in a better place than the above posts :) Please note I am playing on normal difficulty, so this may not work if you are playing hard etc. I hope it helps.

1. All of winter, build up your army with as many Line Infantry as you can afford, add some Spear Levies and a Sabre Cav if you can afford.
2. Last months of winter move 1 cheap Spear Levy along the road just inside the western border. Also move all of your army, leaving 1 unit
for repression, to the northwest rough path.
3. Springtime. Move your main army north, try to end your move in forests to hide. In around 3 turns you should be within reach of the
NW enemy town. Normally the enemy army is stationed outside the city, but as you army approaches it will move inside the walls. This is
where your single Spear Levy comes into play.
4. Move your Spear Levy north along the road and raid the mine. If all goes to plan, the enemy army attacks, retreat and it will attack
again, taking if away from the town. You will lose this fight, but feel free to use artillary fire if your ships are nearby.
5. Attack the enemy town with your main army, which should now be unguarded. If your Geisha is nearby, distracting the garrison makes
thing even easier. Make sure to have your ships in range, so you can bombard the city gates for a quick attack.
6. The town is yours, repair any buildings, hire some more troops. The enemy wont attack you, but will raid the province's resource
buildings. Harass the enemy by bombarding with your ships. Once you're strong enough and the enemy is weakened, go for the kill.

Next, improve your army, because the enemy in the north part of the island is marching an army south. Move your main army east, but
keeping peace in your new town can be a challenge, so leave some crappy troops. When the nortern enemy army moves south towards your
capitol, move your main army north to take over the now undefended enemy town. In the meanwhile recruit more troops in your capitol and
recruit an assassine to get rid of some enemy generals. Once I conquered the enemy town, the enemy force disappeared. If they dont
disappear, combine your armies and attack.

Now move on east towards the last unallied clan. At this stage the eastern enemy force often goes north to conquer the mainland
provinces. By delaying this force's return with my assassin I could easily take over its town while it was undefended. Sometimes your ally
comes along with an army, make sure you are at the enemy city first and lay a siege so you occupy the town once won.

Next.. up to you - break alliance? Conquer the mainland? Cash up for big improvements?

Good luck