1. Claim your base
This is another base defense mission were you'll be weathering a Protoss assault as your Laser Cannon rips through A huge stone door. The mission begins with a few ground units, push forward and kill the scattered Protoss forces; Swann will then send you two siege Tanks and you'll get a short tutorial on how to use them. Press forward and reclaim the base.
2. Set up you base defense
Do as Raynor says and set up a bunker and a Siege Tank at each of your base's entrances, manufacturing some marines to fill the bunkers up. Immediately build an armory and start researching vehicle weapon tech; Siege Tanks are supremely powerful in this mission and teching them up will be a huge benefit.
3. Abuse the laser drill
Eventually you'll be given manual control of the laser drill. Use it to take out the Protoss Archons and Colossuses before they reach your base. Your map will glow red and alert you when there is a high threat target waiting to strike. The Canon automatically resumes firing after you target it to kill enemies so don't worry about re-aiming it.
4. Solidify the base defense
As your resources pile up build additional siege tanks and place them at the points indicated, aim for a bunker and 3 siege tanks at each choke point. They'll have maximum damage here and any enemies they don't manage to kill will easily be handled by the bunker. You can supplement the line with marines and Marauders if necessary, but as long as you take out the high threat targets with the laser, the Protoss won’t stand a chance.
5. (Achievement) Capture the Protoss Relics
This should leave you with a ton of extra money that you should use to build a Starport and 4-5 Vikings. Your laser cannon can't directly shoot at the Protoss ruins unless there is a friendly unit nearby, so send the Vikings out to spot them. Each ruin is very lightly defended with only one proton cannon which the Vikings can easily avoid or destroy. Convert the Vikings to assault mode to pick up the relic from the destroyed structure.