Right when you start out, move your 2 Vultures next to the Supply Depot cluster at the northern end of your base. 
Then, start gathering and get defenses on all 3 entrances to your base: the bridge to the southeast, the multiple ramps leading to the Zerg base, and the pass to the southwest. Even though you can't attack the Zerg base, Zerg units will carry out many attacks against you. It is important not to use Siege Tanks against the Zerg as they may destroy Zerg buildings, and don't have SCVs wandering near the Zerg base because Queens will just Broodling them. Also build a few Missile Turrets and a Bunker behind your minerals as Protoss Shuttles will try to land Zealots there.
For this mission, you don't need many upgrades. Just upgrade the Infantry Weapons and U-238 Shells so your Bunkers can be more effective, and maybe Vehicle Weapons for any Siege Tanks you have defending against Protoss invaders. Build 3 or 4 Starports, and begin building Battlecruisers. 
Be sure to have the Yamato Cannon and Colossus Reactor upgrades. Have 8-12 Battlecruisers ready. You might need to build another base for minerals or gas. There is a geyser near the center to the west, and at the far west between the Zerg and Protoss bases is a large mineral deposit.
After your Battlecruisers are finished, get as many Ship upgrades as you can, preferably to Level 2 or more. When your upgrades are done, move your Battlecruisers to the southwest corner of the map. Proceed eastward along the bottom of the map, wiping out the Protoss base. 
Be sure to Yamato Cannon Protoss Dragoons and Photon Cannons. As soon as the first base is destroyed, return to your base for repairs, giving your Yamato Cannons time to recharge. As soon as you are done repairing, move east from your base, taking care to avoid the Zerg base. Proceed to destroy the Protoss base. After the Protoss are dead, a massive wave of Zerg will attack, and the mission will end.
