[reviewed/revised 16 Oct 2021]
You are supposedly allotted only 9 brigades for this battle, although in reality you can get up to 11 if you have that many in the corps you’re using. You need probably only half that.
It is best to use all infantry or infantry plus 1 cav for capturing Union supplies. You will start the battle with just two brigades.
Take those two starting units south but stop well short of the flag on the hill. Watch out for skirmishers/cav and wait for reinforcements from the W edge of the map. When those come, about a half-hour into the battle, maneuver to the hill and with your greater numbers of units flank the Union brigade or two on the hilltop out of their positions. Take the flag and defend against attacks from the S and W.
Late in the mission a Union force will appear from the north. Use the copse to the N of the hill and the NE edge of the hill to rout brigades that try to cross the river.
Not much to this one, really.
J&P Rebalance Mod (1.27.4.3) BG
The same strategy works when using the mod, although CSA will have 13 units total, so you may be tempted to go for an annihilation of the Federals. Certainly you can wipe the initial Union forces off the map, and with melee cav, can also destroy the Union artillery batteries that arrive from the N among the late-battle reinforcements.
โ โ โ