Okay, on the bright side, this gun finally showed up for me. I had to revisit the Stranger 4 times on the PS4 (where I haven't been playing) before she'd give it to me... but whatever.

Here's the fun part. Once you get the catalyst, you have to defeat 700 enemies with the gun in order to activate it.

The gun's perk is a time portal that shoots bullets from an alternate timeline - it activates after 10 stacks of Rewind Again (which you earn with precision shots). (The catalyst increases the frequency of these bullets.)

The kicker? Enemies killed by Time's Chasm (the perk, bullets from the alternate timeline) DO NOT COUNT towards the NTtE catalyst requirements. Apparently, it's not YOUR gun that's shooting in that alternate timeline.

My early experience (and this depends on your accuracy and the level of your enemies, so YMMV) shows that this perk steals about 20% of your kills. Making that 700 kill requirement closer to 850.

WHEEEEEEEEEEEEEEE

(On the plus side, once the catalyst is done, that perk is gonna mean you're 20% more efficient - and that's a good thing. It's just getting there that's a pain in the ass.)