ancient Civilisation cores not dropping

[Jaynna/Tali]

I've done the Bellanoir raid boss 3 times but only got the Ancient Civ Core the first time. How else am I suppose to get them? I've tried doing the harder ones but i'm not strong enough, do I have to wait till then for a second one?

[Suzaku]

You can also get them from high-level expeditions.

[Halvos]

You get them from the expeditions you unlock after beating Victor and Shadowbeak. That said you should be getting them, the only reason you wouldn't would be if your pack is full in which case they'd fall on the ground when the raid pal is defeated.

[Cheato1]

The level 55 rig can drop em and can be cheesed to get some of the chests pretty early, can also use the meteor launcher to great effect to clear the rooms with the chests if you need to. Not easy but possible as early as level 10 or so.