If you are like me, you may be struggling with the progression of The Perfect Fifth in the Polaris Lance catalyst. I was confused by it, thinking that getting kills with the exploding shot would work, but it is the burn damage from the explosion that actually counts.
A good place to farm this is in the moon corrupted Expunge Mission: Styx. During this mission there are Harpies that spawn with a yellow HP bar. These are the ones you want! So what you do is get precision shots against the ads around the Harpies, and once you have the Perfect Fifth ready, fire a precision shot at the Harpies. The explosion leaves them with very little HP and the burn damage kills them. There are like 8 or 10 Harpies in total.
I farmed this Expunge mission like 7 or 8 times last night and I was finally able to complete the catalyst, which honestly makes Polaris Lance even more awesome. I recommend it especially since scout rifles are getting a buff next season.
Hopefully this helps! Good luck guardians.
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I finished both this catalyst and Graviton Lance at the Altars of Sorrow.