5-8% Strength for 4.5s on Kill. Stacks 5 times.
2.5-4% Bonus Critical Chance on Chained Hit. Stacks 5 times.
-8.5--5.5% Charge Time on Chained Secondary Attack. Stacks 3 times.
Suppress Enemies within 5-8 Radius on Close Range Kill.
This is a build I've been tweaking as I play more and more Pysker. I have about 80 hours with Olivia at the moment and this is the best build I've been able to come up with for myself. Your mileage may vary, I doubt everyone plays the same way I do.
This build is mostly focused on horde-clearing, dropping far away specials while behind cover (snipers and gunners mostly), and giving covering fire for those interacting with stuff.
Your main goal is to take out the hordes of Poxwalkers and other lesser enemies that will swarm you and your team. If you use your Purgatus staff effectively, you can get 800+ kills in a standard Damnation game. Keep your peril high to get a large boost to damage and roast them before they can touch you. Stay in cohesion with teammates and you won't have to worry about using Brain Burst to build stacks, the Purgatus will do that for you.
Keep in mind you have very limited range. Between the flames and the sword, you have no real ranged. Use your Brain Burst to take out distant enemies, especially Snipers and Gunners that might cause issues for less keen eyed allies.
I am still deciding on what I want my second Blessing to be, but Terrifying Barrage seems to be extremely helpful when dealing with a mixed horde. If you're taking las-fire from some Scabs while being swarmed by Poxwalkers, it seems to do a good job at keeping them both at bay.