I completed the first 5 Episodes of Spartans on Heroic, and did not gain the achievement. I did them all online and the game even shows i’ve completed all 5 chapters in all 5 episodes.
Try replaying any mission on easy solo, cause i had the same problem as you and this fixed it. Hope this helps 
I appreciate it. I guess I’m just going to have to suck it up and re-do them. I have this same issue with Halo Reach’s solo legendary achievement.
My achievement didn’t unlock for me either. Kinda sucks, a lot!
if you’ve completed the Spartan Ops missions, and the achievement did not POP… then just replay ANY ONE MISSION ON EASY!
The achievement will then pop once you finish.
You don’t have to replay them all, just one.