Build railways
Railways are so expensive, and require such a level of infrastructure, that they only come into Fall of the Samurai towards the end of a campaign. If you get a line up and running, you have an enormous advantage. Troops and agents can travel from one end of a route to the other in the space of a single turn.
This will let you respond to invading armies very quickly. More importantly, it'll let you get new units, cannons and gatling guns to your forward forces almost instantaneously. The cannon factories you'll need to build gatling guns have to be upgraded many times and take a long time to build. You're not likely to have many, and they'll probably be tucked away safely in the middle of your empire somewhere. Unless you have a railway, getting these monstrous weapons to your armies can take a long, long time.
If an enemy takes one of the stations along the line, you won't be able to transport troops to any location beyond that station. As you'd expect. Trashed stations are very expensive to repair as well, so you'll want to make sure they're well guarded. Conversely, you'll want to break enemy stations at every opportunity, using bombardment, agent sabotage, or ordinary troops.
Look after your Generals
Fall of the Samurai's campaign spans a relatively short amount of time, which means you won't get the problem that could crop up in larger Total Wars like Empire, when leaders tended to die of old age on the eve of an important battle. In this expansion, your generals be there until the end, as long as you keep them out of trouble.
With each battle they survive, your generals will gain experience. As they level up you can buy advances from their personal skill tree, improving their ability to command in the field, or turning them into masterful siege warriors that excel in defensive situations. Keeping your leaders safe in battle can be a delicate business. Their "rally" and "inspire" abilities are tremendously useful for those moments when you need to give nearby a troops a much needed morale boost, but generals must stay close to the front lines to use them. Keep spearmen at your leader's flanks to protect from enemy cavalry attacks and equip give his bodyguard revolvers when you can. This will let these elite warriors deal damage from a short distance, just out of harm's way.
The campaign map is almost as treacherous as combat for your brave generals. Enemy Shinobi can assassinate them outright, and high level Geisha can woo them away from your cause. Use your own agents to counter these threats. Install your own Geisha in your biggest armies to keep morale high, and counter Shinobi with Shinsegumi, Ishin Shishi and Foreign Veterans.
Guns are great
Archers can compete for a time, but in the end, guns will win out. If you're used to meatgrinder melees then the stand-offish art of mid-range gun combat can seem a little odd, but the rules are simple. Focus fire on weaker units to break them quickly, this will have a negative impact on troops near the fleeing unit. It's hard to stand and fire when your friends have turned around and started running for the nearest pub.
Royal Marines, US Marines and infanterie de marine units are very powerful. They're very accurate, reload quickly and can even put on a good show when they go toe to toe. They're well drilled, too, which means they're less likely to break. If you get the opportunity to recruit these chaps through international trade ports, you won't regret it. Shogunate Guard and Imperial Guard are good all-round gunners, and support these quality elite troops very well.
When you can, grab the high-level "kneel and fire" ability. This will train the front rank of a unit of gunners to take a knee while firing, bringing more guns to bear on your oncoming foe. Wait until the foe is just entering rifle range, throw down some artillery and enjoy the spectacle as your troops mow down the enemy army. In the face of all that gunpowder, the Samurai were doomed to fall.
