So I completed everything under par time on legendary and it didn’t unlock. The way I got it to pop was to load in to Lone Wolf on legendary solo and it popped straight away so if you'r having an issue try this!
For anyone who needs help on any specific level I used Vodred's guides which I've posted below. He breaks down the sections and the tricks. Please give him some love on YouTube!
I personally found some of the things like the skips of exodus and the pillar of autumn skips to be massive time savers for the runs. I'll post each video at the end so you don't need to search for them individually.
I can also confirm that you can mix solo and co op times for this and it doesn't need to be done in one run. If you add up all of the par times its 2 hours 35 minutes so don't worry if you're five minutes over on a few of the missions.
Some additional tips from my personal experience: I wouldn't bother with the final skip on the pillar of autumn as its quite difficult to execute, doesn't save too much time and unless you do it perfectly you'll miss the drop ship anyway!
Also New Alexandria is much easier in co op. For example at the hospital get player two to wait by the door at the top. Once you hit the jammer kill yourself and skip that section. Same with the buggers - wait in the elevator and for the hunters you can try to sprint and hit the jammers instead of fighting them and use your buddy as a spawn point.
Hope this helps everyone out! Any questions please feel free to shout.