This is a video I made using cheats to show how much damage the shotgun does to Shrek at different ranges, and what kind of kill strats can work. This is not a tutorial for how to do a quick-kill.
Shrek starts with 8000 health so I use cheats to set his health to 18000. That way he would die if his health falls below 10000.
The shotgun fires 11 bullets in a random spread, which do 120 damage each. This gives a total possible 1320 damage per shot.
The zoom-in sight increases the accuracy of the shotgun. You can tell how much better it is in the video from mid-range. At close-range the shotgun is accurate either way, and at fairly long-range they're both inaccurate enough to not bother with them. But at mid-range the sight gives a big improvement. Mid-range is about from the first soda-boxes to the ground after the swamp.
With 6 perfect shots to Shrek's 8000 health... 1320 X 6 = 7920 8000 - 7920 = 80 Shrek is left with 80 health. Almost anything else would kill him. This makes getting a small hit on him from the cliff very good.
You can cancel reloading the shotgun by sprinting immediately afterwards, which I use in this video.
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Normal enemies each have 200 health.
Damage data: Knife: 110 Handgun: 150 (Full clip: 150 X 10 = 1500) Shotgun: 120-1320 (Max damage full clip: 1320 X 7 = 9240) Slot 4 Machine Gun (in accounting): 50 (Full clip: 50 X 60 = 3000) Slot 5 Machine Gun (in crossroads): 180 (Full clip: 180 X 30 = 5400) Slot 6 Machine Gun (used by enemies): 160 (Full clip: 160 X 30 = 4800) Sniper Rifle: 400 (Full clip: 400 X 12 = 4800) Sword: 200
Enemies can hurt each other and Shrek while shooting you. They do as much damage as they would to you. Lying prone next to Shrek with lots of enemies around him, he lost 100 health after about 6 seconds. This is not nearly enough to be useful in a run.
Headshots do no extra damage, neither to Shrek nor normal enemies. Explosives do no damage to Shrek.
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I used Cheat Engine to get this data: http://www.cheatengine.org/