Daxil asked me to write something about my strategy so here it is.
First as Union:
Frozen weather at turn one around Memphis told me there will be no rapid advance so I decided to strengthen up and move when weather improve. After battle of Corinth where Union army of 50000+ lost to CSA army of 25000 I decided not to waste time with well entrenched rebels and went for weakly defended Chattanooga. In the meantime Butler arrived at New Orleans which was defended by rather strong force under Polk. Landing there was out of the question so I decided to knock out forts first to get supplies, points and clear the way for navy than turn on Mobile. That drew Polks attention who left New Orleans practically undefended and Dodge with some 3500 troops seized the opportunity. From than on it was basically playing for points by holding objectives and strategic towns. At last couple of turns I managed to take Memphis and even capture Beauregard's HQ but Breckenridge escaped engagement twice.
Weather at turn one this time was exactly opposite of previous game, nice and clear. There was no time to dug in and bring troops so eventually I abandoned Memphis and massed at Corinth. I lost battle there but managed to inflict heavy casualties on union army which bought me some time. From than on it was buying time with defensive retreat and with sending raid parties to Union rear to hamper supply lines. I knew that Union army will have problem with supplies. If I'm not mistaken some 30000 Union troops perished due to lack of supplies. Than I noticed that Grant HQ is almost alone at Memphis. Breckenridge with one division after forced march have taken Memphis but Grant escaped. Now my plan was to withdrew down the Yazoo River but than I realized I'm going to have a huge problem mostly because of my inexperience with this scenario. I counted on Vicksburg batteries to stop Union ships going up the Yazoo river but that didn't happen. Those batteries haven't done a single bombardment not only of ships moving up the Yazoo but not even of two ironclads from Farragut fleet moving up the Mississippi. Don't know if this is the case just with this scenario.
Aryaman, thanks for good games. I've learned quite a bit. There was moments I thought I'm not going to make it. You are right, this scenario is too short to go after CSA army. It would be nice to continue, too bad it's only 24 turn scenario.