Weurgh, I just managed a BV last night. It was quite a phyrric victory - I lost many units and ended up with a single mechanised infantry unit in Stalingrad, cut off and surrounded by a sea of red. If the AI had been a bit more proactive in shifting stronger units to defend the objectives I wouldn't have made it. But, I made a net profit in terms of prestige which is the important thing at the moment! I'll come back to it later and try and win a clean victory once I've completed the campaign
A few things I found while playing!
The two bridges in the centre - one of these crosses into a swamp, which is bad. Several times I was seduced by this bridge, as it seemed the quickest way to unite the centre with the south and encircle a ton of infantry, but the swamp just stalls all your progress. I found it much better to use the other bridge.
I think the Soviets start with a huge veteran T-34 division, this thing is beastly so you need to smash it. If you get the opportunity, dump both your airstrikes on it and chase it with some panzers.
I increased supplies on the most northerly supply point, and used the allied mobile/infantry units and some Germans to defend the supply route. Keeping this supply route open also keeps a large portion of soviets encircled, negating them. This scenario also taught me to cycle my units in and out of supply. Also the importance of still being able to fight one turn out of supply - your one supply drop can keep two units fighting (just about).
Finally, don't be afraid to disband a unit if it's out of movement points and impeding progress. Sometimes I would use a Mountain to try and finish an enemy off so my tanks could push right through, only to have my Mountain fail. Disband him, and get those tanks rolling!
One final note, on my first attempt at Stalingrad a couple of days ago, I spent the 270 prestige needed for the Grenadiers. They're amazing, you can pretty much derp your way from the south into the City. If you're having trouble and simply want to just get past the mission with a DV then I reccomend them