The key to Challenge 1 for the shotguns is hitting as many targets as possible with a single slug. To do this you will need to move your character as well as your aim. Aim at an angle and line up as many targets in your crosshair as possible. Use the assault shotgun to get gold in this challenge, however you will need to complete the challenge once before you can use the assault shotgun.
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The key to Challenge 2 for the shotguns is hitting the center of the targets. Wait for the targets to get close to you before shooting them. Use the assault shotgun for this challenge because you won’t have to reload the assault shotgun during the challenge.
The key to Challenge 3 for the shotguns again is hitting as many targets as possible with a single slug. In this challenge the targets move into a position that makes it easy to hit many of them with a single slug. Use the assault shotgun to get gold in this challenge, and wait for the perfect moment to shoot.