After the cutscene, as soon as you gain control over Frank, take cover behind one of the display items. As you have surely noticed, Cletus is packing a shotgun. This is bad news for you, as the Shotgun is a very powerful weapon that can knock off large chunks of health. Try your best to remain in behind one of display objects while Cletus is firing. However, even if you are behind cover, you can still take damage, since the shotgun fire spreads.
Only pop out from behind cover to shoot Cletus while he is reloading. This is your window of opportunity. Don't stay out in the open for too long though, because Cletus can reload his shotgun quite quickly. Another chance to get some shots in is when Cletus stops to take drink some Wine.
Don't even try to melee this guy, because if you get too close, Cletus will pick Frank up and throw him into the middle of the store, dealing a significant amount of damage and leaving you open to a shotgun blast.
If you are low on health, take cover behind one of the display objects and consume a food item from your inventory to regain some health. If you didn't bring a Handgun, you can smash the display case in the middle of the store to find one.
Alternatively, if you're the daring type, you can attempt to jump over the counter and grab a Sniper Rifle or shotgun. If you can manage to get your hands on either a Shotgun or Sniper Rifle, it will surely help. If you can take the abuse, go for it. The Sniper Rifle is the better choice, as you can use the scope to score some easy headshots. If you manage to get a Sniper Rifle and leave the store, you can shoot Cletus through the open double-door while remaining relatively safe.
If you want to go this route, hide behind the one of the store displays near the counter until Cletus is forced to reload his weapon. At this point, make a mad dash for the counter, hop over, and grab the Sniper Rifles from the rack on the far right. Only make this attempt if Cletus is standing at the other end of the counter, otherwise you likely won’t have enough time to grab the weapon. Once you have the weapon, try to hop back over the counter and run for the exit. You will need plenty of healing items in your inventory to make it through this, as Cletus will likely be able to blast you a couple of times before you manage to exit the store.
There is a mob of zombies just outside the Huntin’ Shack, so switch to a melee weapon and clear away as many of them as you can. Or, if you have a Queen, use it. If you are in dire need of healing, get into the corner, away from the Huntin’ Shack double-door, and consume a food item. When the zombies outside of the store have been dealt with, stand back as far as you can from the open door. Switch to the Sniper Rifle and start hammering Cletus with shots from afar. The aiming is a bit jerky, but try your best to hit him in the head.
Cletus’ Shotgun boasts impressive range, so you can still take damage here; move away from the door and use a food item from your inventory if your health is very low. If Cletus won’t stop shooting through the door, head down the hall until the music stops, and then head back to the Huntin’ Shack entrance and with any luck he will have calmed down.This video is from our unofficial game guide. You can view the full guide here