How do I get past the dogs?

[LegendExeter]

I've found in either game mode, the arena or vault defense when making a legit run I cannot get past the dog wave about 20 minutes in or 8 minutes in on vault defense.

 

The video showing how on YouTube is from Xbox and doesn't have the dog wave.  There are too many, they are too fast, and they do a lot of damage.

 

What key perks or strategies do I need to get past them?  I had XP bonus, Hybrid, and Light as a Feather and they were just a swarm all over the place.  Is this a point where I just go to a safe spot and hope?