I can't get Gunslinger Challenge kills to count while in Showdown?

The poor bullet speed of Torgue gyrojets may be the reason

Citation of the official fandom:

When Showdown is triggered, Nisha will lock on to nearby targets, providing automatic aim. The auto-aim doesn't take into account critical hit locations however, opting instead to target an enemy's 'center mass', unless sighting down the gun sights in which case the critical points are targeted instead. Each time a target is eliminated, a new target is automatically selected. They can also be cycled manually.

Given that, you should be able to score crits in showdown, even with a Torgue pistol that all suffer a minor lack of accurancy, but the recoil reduction boost of Showdown should even that out pretty much. A Thick Slapper can outdamage an Ornery Iron of same level and rarity and performs better against armored enemies, due to the explosive bonus damage and should therefore suit to fulfill this challenge. However the time between a projectile being fired and it actually hit the target counts against the timespan in which you can score this challenge. Given the slow travelling speed of the gyrojet projectiles all torgue pistols will suffer from that flaw as the increased bullet speed mod is not available on pistols.

Jakobs guns in general have the highest bullet speed. Vladof, Dahl and Hyperion can also perform well, tho the Showdown mechanic works best with Jakobs weapons as the recoil reduction boost would be rendered useless on Dahl and be even contraproductive on Hyperion as it prevents them to increase their gross base accurancy via their reverse recoil mechanic

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EDIT

I oversaw that Showdown increases bullet speed by 50 % also. However, this may not be sufficient, as 50 % faster than awkwardly slow can still be too slow. The timespan between aiming down the sights, firing a shot and giving your target the final blow is indeed very short.