You can start right off with the bombers to destroy the artillery position to the north, or take a moment to build your base. I chose the latter. I recommend building a refinery to place at the southwestern tiberium field. Don't bother building any additional air units as they can not be used to much effect in this fight. When your base is advanced a bit, clear the artillery from the map.
The map will expand, revealing the additional artillery emplacements. You will be given access to stealth tanks by Kane personally. Additionally, you will be informed that the artillery to the east is primarly guarded by anti-vehicle weapons and features heavy air defense. Naturally, you should exploit their weakness to infantry and produce eight black hand, ten missile squads and four shadow teams. While they are training, make numerous flame and scorpion tanks to defend your base. Use the assault move command on your infantry and flatten everything on the way to the artillery. While they are on their way, order you base to produce about ten fanatics. Destroy it, then prepare to reinforce them with vehicles you have been producing from your base. In all, shoot for six flame tanks, six scorpion tanks, eight black hand, four shadow teams, and ten fanatics. Replace any infantry that were lost and rally your forces at a safe distance from the GDI base in the middle (secondary objective) and attack from the southwestern side.
Send the fanatics in first to soften them up, then use the attack-move order to unleash all kinds of hell upon their defenses. When the base is destroyed, or soon after, a convoy will arrive that you must destroy before it reaches the base (secondary objective). Get some units on the road that is all the way on the eastern side of the map and guard there for the convoy. A few flame and scorpion tanks will do just fine against the zone troopers that guard it. Additionally, there is an aircraft carrier on the southeastern corner of the map that can be destroyed (bonus). With that done, send a final group into the third artillery tower, which must be lacking power for defenses with its supplying base wiped out.