Overview
The Russian army holds an excellent position, with powerful artillery on hills an rivers as obstacles. Winning this battle requires a lot of manouvering and micromanagement. I will split this battle into three geographical areas: North, Center and South. Pause the game/set the game to slow often during this battle to manage everything on time. The longer you take, the more time the Russians have to punish you with their artillery.
While I am writing this in three separate parts, it's important to try to do all three parts of the battle at once.
North
This consists of the Swiss Foot, Chasseurs à Cheval, Cuirassiers, and the Chasseurs and Fusiliers of Line furthest north. The Russian forces in the area are (initially): a unit of Russian Jägers, a regiment of Pavlovsk Grenadiers, and some cossack cavalry/hussars.
The A.I controlling the Russians *insists* on having at least a few units in the northern town. If it loses too many troops there, it starts sending troops from other parts of the battlefield there. Therefore, the more units you can kill off here, the more you weaken the Russian army elsewhere.
The Pavlovsk Grenadiers retreat into the garrisonnable house close to one of the river crossings if they take too many casualties (about 50), where due to the combination of their excellent stats and the very hard difficulty, they can be impossible to flush out or ignore. Routing them before they can garrison is imperative for controlling this part of the map.
Send the cuirassiers further north and have them cross the river, after which they move to a distance away from the Russian Jagers (but not close enough to aggro them). Meanwhile, have the Swiss Foot and the Chasseurs move into the forest to the east, while the fusiliers move to the north to meet up with them. Use the Chasseurs to lure the Pavlovsk Grenadiers across the river. Constantly and gradually pull back each of the troops whenever the Pavlovsk Grenadiers get close enough to fire. Once you have lured the grenadiers out of the forest, have all the infantry fire on them while the Chasseurs à Cheval charge them from behind. This should break the grenadiers. Send the swiss foot or fusiliers close to the Russian Jägers, to convince the Jägers to shoot a volley. Simultaneously, charge the cuirassiers into their back. Put the fusiliers and swiss foot in square formation, and position the chasseurs in a way that allows them to deliver fire on the river crossing while being close to the squares. The Russians should send their cavalry to help their jägers. Pull your cuirassiers through the jägers and to the safety of your squares. The Russian forces should get destroyed by your squares and chasseurs. Any remaining cavalry can be lured into your squares with careful planning and timing.
With the cavalry dead, the enemy general is defenseless. Send your remaining cuirassiers and chasseurs to rout him. Have your infantry in the north focus down the Russian infantry they send over one regiment at a time.
If you don't do well here, don't fret. If the Russian center and south fall then the troops they have here automatically start breaking.
Center
This consists of all your artillery, and the chasseurs between your artillery.
Unlimber all your artillery. If you don't, they'll start dying off anyway due to the very accurate Russian artillery fire. Your 12-lbers are more or less useless offensively, because they are in a ditch and don't have a good angle on practically anything. The one exception is, possibly, the house next to the pavlovsk grenadiers to the north.
Your 6-lbers should start targeting the ground in front of the 20-lber unicorns. This allows them to hit the unicorns, the grenadiers behind them, and the opelchenie and cossack cavalry behind them. This collateral damage can be very handy--by the time I got to them, the cossack cavalry were already routed from the stray cannonballs.
Your chasseurs should go into light infantry formation and make a beeline for the same unicorns: they can shoot at them from the other side of the river. RUN there to minimalize casualties.
Your artillery will take casualties. It's inevitable. Whenever they rout but then stop running, send them back to their guns. The longer they distract the Russian artillery, the less your other troops have to suffer.
The grenadiers protecting the 20-lbers begin chasing your chasseurs. After the 20-lbers are broken, use your chasseurs to lure the enemy grenadiers back to your cannons, who can use canister shot to rout them easily. After this, the chasseurs can be used to assist the southern army.
South
This consists of all your remaining troops: Napoleon, the rest of your cavalry, and a large number of fusiliers, grenadiers of line, chasseurs, and a polish legion.
The chasseur regiment closest to the 20-lber unicorn goes into light formation and heads for the 20-lbers to assist the other chasseurs in taking it out. Everyone else heads toward the forest in the south. All the cavalry then move to the south of the southern town.
You'll be dealing with a lot of individual regiments of Russian troops. Use your chasseurs and fire a volley at them before running away and luring them to your fusiliers. Try to mix in a charge from your cavalry from the flank or rear if you have the room. Move a grenadier or fusilier regiment close to the enemy cavalry to provoke a charge, and then form squares to fend them off. Use your cavalry to charge enemy artillery when they're no longer defended by infantry, and so on.
In this manner, gradually work your way north. You'll eventually reach the center of the Russian defenses: the indomitable Raevsky redoubt. If your northern group has been doing very well, then the Russian infantry should have abandoned this redoubt to reinforce the north, allowing your cavalry to easily charge up and wipe out the artillery there. If not, you'll need to lure the infantry down and pounce on them before they have a chance to run back up hill.
Once the artillery on the redoubt are dead and the general is dead or has fled, the remaining Russian troops should flee.
Final Thoughts
After the initial annoyance at the Russian artillery, I came to greatly enjoy this battle. The micromanagement was a good deal of fun. While I had to pause often and that took the immersion out of it, it was fun watching the battle afterward in standard time.
The battle is also probably the first instance in which the game fully demonstrates just how highly the Very Hard difficulty tilts the battle in the A.I's favor. In any 1 v 1 situation, your troops will get crushed by their Russian equivalents. You HAVE to attack any Russian troops with at least a 2 to 1 advantage, ideally more, and hope that they break before they get too many volleys off. The Russian Jagers also had the curious ability to shoot out the back of their heads to protect their rear, as my cuirassiers brutally learned to my horror in an earlier run of this battle.
The battle is not as hard as the forums might make it out to be: a vast majority of the Russian troops are tied down to protecting their artillery, giving you a huge mobility advantage and allowing you to easily exploit your light infantry advantage. That being said, the Russian artillery are extremely deadly should they start attacking your non-artillery troops, and things can start looking gnarly quickly.
I give it a difficulty rating of 3/5, which is not something I would have said upon beating it for the first time. The fact of the matter, though, is that the majority of the Russian forces pose no threat to you since the A.I causes them to be locked in position until it's too late. As long as their artillery remains focused on yours, and they should, you should be largely ok for this fight.