If you run it with multiple persons you just need to run it again (the person who didn’t get a core). Just run through to the exit and the mission will finish for that player, too.
Alternatively wait a bit between leaving the mission, let the first person reach EGS HQ and complete mission, step away from the portal and then the next one can go (you need to keep your distance to the portal inside aswell).
Regarding difficulty: Post your (Twitch) streams / (Youtube) videos here!
There are two videos I made of solo runs, watch that if you get stuck somewhere!