[revised 31 Dec 2020]
You are allotted 9 brigades for this battle (best to have all infantry brigades or 8 infantry plus 1 cav for capturing Union supplies) and will start the battle usually with two.
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. When the timer hits zero you can continue the mission—I’m not sure how long—and it makes sense to do so if you’re in good defensive positions and steadily wearing down the Union numbers.
Not much to this one, really.
The basic strategy I have outlined above also works for this battle when using the J&P Rebalance Mod. However, when using the mod, always check ahead for the numbers of units you can bring to each battle. In the version I have tried (1.27.1a) CSA can bring 13 units.