I am making a series of personal strategies and experiences complementing the historical battle pages of the games I have played. Starting with the Battle of Lodi, the first historical battle in Napoleon: Total War. All battles are played on hardest difficulty.
Overview
Napoleon's army starts with his army deployed in the southern side of the map, overlooking the town of Lodi. I immediately rush all my infantry toward the town, and move my cavalry toward the north-west. I unlimber my cannons and immediately begin target-firing the house on the south-west edge of the town, as it is garrisoned by Austrian troops early and I don't want to waste men fighting to take it.
The cavalry attack the landwehr that are on the western side of the map and are trying to escape east. After the charge, the cavalry continue running west to intercept the grenzers. The Chasseurs à Cheval make for the northernmost crossing of the river; after they get to this crossing, they cross the river and intercept the Austrian general, Beaulieu. I ran my chasseurs à cheval the entire way. Beaulieu's troops don't fight or even react to your shooting them so their stamina isn't important. The dragoons can cross at a more leisurely pace, and then work to destroy the Austrian cannon on the east bank.
Meanwhile, the light infantry engage at a safe distance from the enemy troops, and after they get a volley or two off, have the friendly line infantry overtake them and start focusing the Austrians down. In this manner, a good half of the Austrians can be wiped out before they can group up. After taking out the south-west building, the horse artillery can either start firing on the troops from a distance, or one or two of them can run into the town, unlimber, and use canister shot (the lone regiment that has the Barrage ability would be ideal here). While this strategy is effective, care must be given to not have the horse artillery stray too close to the enemy infantry. Meanwhile the light infantry and grenadiers move into the town. The grenadiers can attempt to use their grenades in the close quarters, though I found that this has mixed results.
With Beaulieu dead and the Austrians being harassed by canister shot and musket fire, the rest of the Austrian army should rout.
Final thoughts
Being the first battle, the Battle of Lodi is also in many ways the easiest. Even if the Austrian army were to face you head on, most of their troops are very weak and easily defeated. Many of the Austrian forces ignore the French troops even when fired upon, allowing them to be weakened and destroyed before they cross the river. Johann Beaulieu takes an extremely long time to escape, to the point where not catching up to him may be considered a more impressive feat than stopping him, and the mass rout that happens afterward makes mopping up a cakewalk.
I give the battle a difficulty rating of 1/5. It's frankly difficult to lose this one.