I get your frustration, but just thought I'd point out in case you were unaware, just wait to do the pvp part of the catalyst quests until you've leveled up the season pass. There's boosts in the pass and you end up only needing around 10 or so kills with the boosters.
Also wanted to mention you can equip the sidearm and go into the team scorched playlist and get the kills there, I don't think you actually have to get the kills with the sidearm itself, just have it in your inventory.
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Part one of the quest you just need kills with the gun equipped, but part 2 needs kills with the gun itself.
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I completed the first part without even having the gun equipped.
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Ah I see, I haven't even started yet just going off of previous quests. As a pvp player I'm actually happy when I can do stuff in pvp but I absolutely understand why people hate it.