As many people have mentioned, this achievement is pretty buggy. No one really knows what truly does or doesn't work to get this, so I'll just post what worked for me and my buddy after 3 other attempts following the guides.
* Host (me) selected the challenge.
* Only host collected the large/medium artifacts.
* Partner followed me into the tombs while I collected, but I don't think this is necessary. Just did it to be safe.
* Host collected 6 large and 3 medium artifacts. We didn't collect any small.
* Host lit the signal fire and was first into the blue circle.
* Host used 2 cards to increase animal damage and food. Nothing to affect skills.
We ran at full sprint in a straight line and were able to find the tombs much quicker this way. We raided 9 tombs and escaped on day 10 in 90 minutes. As host, I discovered 8 of the 9 tombs myself. I doubt this matters.
I don't know which parts of these steps are necessary, just that this combo worked.
On the previous two failed attempts, we followed the standard host collection rules, had 5 artifacts in the first go and 6 artifacts the 2nd, at least 2 of which were medium.
On one of these failed attempts, partner had a costume card which granted skills from the tree. On another failed attempt without any cards, I lit the fire when I wasn't host of the challenge. No idea whether these things affected it.
Patience and luck is definitely key.