The achievements in MCC are broken. I don't know if this is an OS issue or specifically an MCC issue but my brother will constantly miss achievements while we are playing splitscreen campaign co-op.
Here is what we are doing:
We started the Master Chief Saga Playlist (play all games starting with Halo 1 on normal). We are doing splitscreen co-op.
We beat Pillar of Autumn. I popped four achievements for 1) Completing any normal co-op level and 2) Par time for Pillar of Autumn and 3) Beat Pillar of Autumn and 4) Beat any level. My brother didn't pop any of those. We had to back out of the Playlist, then redo the level via regular level select and then those four achievements popped for him.
Same thing with the second Halo 1 level. We continued the playlist. We beat the level and I popped two achievements for 1) beating the second level and 2) beating the second level without entering any vehicle.
My brother got the achievement for beating the second level without entering any vehicle... But he didn't get the achievement for beating the level.
That is so frustrating. We decided we are going to just ignore this and perform a mop-up for any glitched achievements AFTER we finish all six games (1, 2, 3 ODST, 360 Reach, and 4).