Ok, how about a different question - can it be done with different partners, or does it have to be with the same player for the whole campaign? Can another player pick up and continue where I left off with the previous partner?
The way the game tracks and records progress is based on each individual chapter.
So you can quit and come back to it on another day. You can do different chapters with different friends.
You can do it with a partner who is playing on a lower difficulty, but obviously only the person with all chapters completed on Hardcore will get the challenge.
You can do the chapters in any order you want.
Basically as long as every chapter has been cleared on Hardcore and Coop, then it will unlock.