Supreme Commander 2

Addition: I reference directions based on the starting view of the mission. I understand you can rotate the camera and that changes perspective, but there isn't much need to rotate the camera for this mission.

This mission is not difficult at all, even on hard. First off, build 5 or 6 anti-air turrets at the north-east corner of your first base near your Land Factory and position an engineer in the middle of them. You will then be safe from attacks pretty much indefinitely. Build up a large force of Wasps and Bombers (ensure you make them hover over the south-east end of your base so enemy attacks don't destroy them), and move to destroy the first objective. You will have lots of time to build more than you need.
Once you gain control of the second base, build 4 ground turrets at the end of the ramp at the north-east end of this base, and position an engineer directly behind them. The enemy will send small, ineffective ground attacks in this direction, but your turrets will mow them down fast and get repaired quickly by the engineer.
If you are aiming for the hidden objective of building a mass extractor on each of the 2 mass spots to the west of the enemy base, just destroy all of the left side buildings of the enemy base and leave the right half alone and send in an engineer escorted by Rock Head tanks and Wasps. Once you complete the objective, the remaining part of the enemy base will fall easily.

Here's a video the mission played on hard by someone on PC. All objectives completed.