I just beat mini Crota with a group of 6. They were randoms to me but I don't know about them, I think at least some had chat. It's basically just normal Crota with a really short timer.
Kill all the adds that spawn and then kill the sword bearer. After someone has the sword everyone attack mini crota at once to stagger him, once he gets up wait until he can be damaged and do it again. You get two staggers per sword spawn and then you just repeat.
Kill adds, get sword, stagger, wait, stagger, repeat. The big problem is a lack of communication between players in CoO. If you're on party chat it should be easy. Also you really need to kill all the adds or the person with the sword probably won't make it. It seemed like only the person with the rune got the fragment which sucks. I got a card and legendary engram though. With chat it looked easy. The problem with randoms is getting the timing right.
Edit: beaten, damn this thread is fast.