Okay, so couple things to take note of:
-You can jump between levels and it will still unlock once you've completed each level at least once on Hardcore
-You can do the above in online co-op thru create a match and selecting the levels.
-It tracks any single player progress you made and counts it towards your co-op progress.
Couple early levels glitched on us, so we had to quit and start again and jumped around playing different levels. I had also completed the first 3 levels in single player, and finished the remaining ones in online co-op, which still unlocked this.