At the start of the mission, 
immediately move your units and 2 buildings around and including Kerrigan to your main base. While they are moving, look at your Supply Depots at the bottom of the map. Move the 3 Marines around them to your main base as a Siege Tank will soon destroy them. Cloak Kerrigan and destroy the tank and the 3 Marines guarding it. Now, start gathering minerals and bunker up your base. At each entrance place at least 2 Bunkers, 2 Siege Tanks, and 2 Missile Turrets. Remember to bunker up the bridge leading to where your Supply Depots were. Also build Missile Turrets all along the edge of your base in case enemy Wraiths cloak and fly in.
When your base is well protected, start gathering massive amounts of Vespene Gas. With your Starport build 6 Science Vessels, and build 11 extra SCVs from your Command Center.
When your Science Vessels have full energy, move them and your SCVs to the resources at the bottom of the map where your Supply Depots once were. Form the SCVs into a line and grab the SCV carrying the Psi Emitter, placing it at the end of the line. Defensive Matrix all the SCVs, and send them in a mad rush toward the beacon at the enemy base. (Should all your SCVs die, which shouldn't happen, you can always simply build a large force of Marines, Siege Tanks, and Goliaths to wipe out the enemy base)
