Got 3 stars on this mission now! Once I realized the troops should support the AT-MP, it turned out to be easier than Rebels.
This basic strategy is similar to Rebel's here: viewtopic.php?f=50&t=1274&p=2693#p2693
Few things different for Empire/Imperial:
1. The AT-MP has nearly equal ranges as most turrets so it can hit buildings from a safe distance, which is important because it does not have much hit points. Use the AT-MP on the right side of the right base once all the shields are down. AT-MP prioritizes shields so if any other shields are still up, the AT-MP will walk right through enemy fire and die very quickly.
2. AT-ST is very strong so it does not need as much troop support. Use the storm troopers to support the AT-MP and Tanks.