Are Halo MCC Achievements based on personal performance?
Yes, those achievements can be achieved by you, if you play the level in co-op and your friend does not play the level according to the achievement criteria.
I have tested this with my brother lately and it is also stated here. There, it also says that you could use local co-op (if you have a second controller) and use Player 2 to play the level normally and get the achievement for Player 1 (actually you), who would just stand around idle.