I've seen many people on TA and x360a say that they have beaten all chapters and checkpoints on Realistic in coop, but did not receive the achievement for completing the campaign on Realistic. GatorFist
and I recently beat RSV2 on Realistic, and we both got the achievement. The conditions we followed every session were
1. I was always the host.
2. Both of us were playing the game from a disc, not Games on Demand.
3. Neither of us played coop campaign with another person in breaks between sessions.
4. Every time we resumed our campaign, I pressed "Continue" at Private Coop Campaign, rather than "Scene Selection."
5. I sent the invite to him during the loading screen for the mission.
While I'm not saying you have to follow these guidelines to get Freedom Shall Prevail, following these gave us the achievement while still letting us play in coop.