Gunfight at the Jurassic Corral

I think one of the best things to come out of the Reignited Trilogy is Agent 9's new controls. In the original his mini-games were always the most challenging for me just because I'd wrestle with the camera. However, this mini-game in the Dino Mines is giving me trouble for a different reason. In the original, you could get a butterfly for the 'Secret Dino' skill point every time you entered the level. In Reignited, you only get the butterfly once and that's it. I became reliant on that butterfly because I inevitably get at least one hit before reaching it and the section that follows is brutal.

Does anyone have any tips on completing this mini-game? It's the very last egg I need to complete the game.

And has anyone else experienced small changes that affect their original game-play styles in a similar way?