The Dig

This mission is broken up into two sections. At first you'll on have a few marines and medics. You'll need to move carefully and take out the few Tal'darim ground troops. Upon arriving at a few Protoss turrets, Swann will send you a new vehicle, the siege tank.

They can enter siege mode, which will great improve their attack range, but prevent them from moving. Move your tanks into range and destroy the turrets and any Protoss. Your ground infantry should stay back to avoid taking damage. You'll soon arrive at a abandoned outpost and a mining laser.

Set up a few bunkers and factories. You'll want to produce many siege tanks and place them in siege mode. A few missile turrets can also come in handy. This mission is about holding out against the enemy, rather than direct assault. Eventually you'll gain direct control of the mining laser and should direct it to deal with strong Protoss such as the Archon and Colossus. When these forces are killed off, return the laser to extracting the artifact.

We the coast is clear, send some tanks and SCVs to establish a second command center and gather additional resources. You can also use the laser to destroy other Protoss buildings, which will unlock research back at your lab. When the artifact is close to freed, the Tal'darim will throw everything your way, so hold out one last major defense.