If you're able to join random games, you don't have to beat the entire campaign on this difficulty. As long as you join before the end of the mission, you'll receive credit. This means some unlucky person could fight through 90% of the mission and you join for the last 10% and receive credit for beating the mission. (Lucky you!) To see which missions you've completed, select "service record" from the menu and select "records". The first highlighted screen (campaign records) will list all 11 missions with the difficulty you've completed. If the cheevo doesn't unlock, try doing one mission solo (mission 11 is pretty easy) to get it to unlock.
Co-op is easier if you have the opportunity, but watch friendly fire especially flame thrower. Enemies are tougher and do more damage. Revives will help a lot along with good communication for solid teamwork. If going solo, use the parts of the campaign where you have help from NPC's to your advantage. You will also have no "HUD" during this playthrough so ammo and reloading can become tricky. Find co-op partners using THIS THREAD.