C-1: Kill all enemies. Pick up the ODST's if you want some help.
C-2: You start with my favorite Armor Ability, Regeneration Field. Not only does this make you virtually unkillable while it's active, it also heals the engineer. I prefer it even over the abilities that cost XP. Use it a lot, and you'll have no trouble.
C-3: Hit and run tactics work well here. Or, use a plasma pistol overcharge to disable a wraith, steal it with X, and kill the other wraiths. If you need to, get out and destroy your own wraith. This level is also where you can get:
C-4: Watch out for the Stealth elites! The needler's slight tracking works well against them. You also need to keep the snipers safe. Make sure you clear an area before moving on.
C-5: I was stuck here for a while, until I discovered a shield Regeneration armor ability in the top right corner. I recommend running for this before you kill the first grunts. The hammer brute can be tough. Make sure you grab the dual SMGs before you kill the first grunts. After that, stick to the engineer. He can die fast on this level.