Once you're a bit into Act 2, Wilson will call you and let you know that he's holding a shooting competition, and that he'll wait to start it until you arrive. Accept the gig, called "Shoot To Thrill," and head to the 2nd Amendment gun shop in your apartment building, the same place you can pick up the Dying Night iconic Power Pistol.
Once you get there, talk to Wilson and he'll unlock the range for you to enter. Walk to the second to last booth, and wait for him to finish his dialogue so you can start.
How To Win in "Shoot To Thrill"
The UI will say 0/100 hits but that's really the "max" number of times you could potentially hit the targets. You'll want to get 41+ in order to win, anything below that puts you in second place.
Since this is pistols only, pick one that has a decent-sized clip and decent fire rate. While each target is individual, you can hit them each multiple times to rack up your score. You don't have to hit dead center, so if you aim toward the bottom, recoil should let you hit 2-4 times per target depending on distance. You have 60 seconds, which is plenty of time to get the 40+ hits you need to win.
I used both a Smart Pistol and Power Pistol, and with both was able to easily hit 50 points in both cases. If you win, you'll take home the shiny new Epic Power Pistol (M-10AF Lexington) that Wilson offers up as the prize, as well as 500 Eurodollars. Not to shabby for some target practice.
That's how to win Shoot To Thrill's gun competition.
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