Focus your base taking only the left side 1st GDI base.

Fly 2 Shadow team into the Left side of the base, i land near four power plants . Dont attack 1st just use it to spy what base defense they got and where their placement of Const,refinery,barrack,factory.

then start order few eng from barracks get ready to have engineer rush. When u move the engineer to the left base try to keep it low on the map as possible to avoid the battles between the gdi vs scrin.Only move eng go into the base...commando and other shadow protect the nod base

When your eng reach GDI base, you can start hearing someone asking permission what to do. When that happens as fast as possible start take over the const & refinery and barracks and factory. Use the const to build of the anti-vehicle defense and start attacking the base defense or units.

from there try to pin down their units...
Start building def for your nod base and the gdi base.
On the top map there is GDI airbase . Use firehawk to attack scrin air units. Then transport rush engineer up there. 

Good luck..

Don't bother moving your Commando or Shadow Team. Crank out enginners and place them next to each of the buildings you are supposed to capture.  (This is just like what Ahmike posted, but instead, you'll be doing the Scrin as well - The Scrin will also not open fire until provoked)

Go into Planning mode (at the bottom of the screen, one of the buttons), and make each enginner capture the buildings. Exit planning mode, and if you do it correctly all your enginners will capture each building at the same time, ending the mission.

The bad thing? You will not be able to complete the two bonus objectives. But if you just want to get this out of the way, then do this.  You also have to be quick, as if they destroy the enemy Drone Platform/Con Yard, you fail the mission.