This is not exactly a guide, but this achievement may be glitched in a good way. I had played through the first 4 missions on Normal and started up the 5th mission. I realized shortly after beginning that for some reason it was on easy difficulty so I quit out to play it on normal and right after I quit this achievement popped without actually completing the 5th mission.
Edit:I just figured out that you can start up each mission and then quit out and it will give you credit for completing it. I did it on legendary difficulty. This should work for each episode.
Edit: According to Recon1O1 This glitch may have been patched requiring players to actually have to play through all of the missions to get the achievement.
Also as a couple of people have noted this achievement tends to stuck and says "Done, Unlocking...". Unfortunately I know of no way to get around this. Yes, you have finished the achievement, but only time will tell when it actually unlocks. This is on either Microsoft or 343's end. I know I had this same problem with many achievements in this game. You just have to keep checking it to see when it actually unlocks. It is quite frustrating.