*EDIT* for what it's worth it seems you only have to damage the matriarch at the moment of this posting with the dropshot relic. Make sure everyone in your party damages her and you will all get it. (see comments)
This can be done solo but much easier with a partner as they can turn the Matriarch around and you can shoot them in the back or vise versa.
Load up Escape on Ice Queen (Escape > Custom > Host Private > Ice Queen Map) At the start of the level take the right path and there will be a Dropshot Relic in the safe room:
Hold onto this and run through the first part of the map. All the Scions have more Ammo and make sure you pick up the Red ammo boxes for even more. Once you get through the Checkpoint shower rooms the next area is where the Matriarch spawns. I would suggest killing all the Juvies and then leading her down away from all the snipers so you can just focus on her.
This is the Matriarch for those that don't remember:
Lower her health to nothing and then hit her with the dropshot relic to kill her. if you run out of ammo just die and you respawn in the shower checkpoint area with ammo.
Note: I helped a buddy get this cheevo and he got it even though the venom killed her after his first dropshot didn't.
Visual Aid: