Since the solutions to challenge #3 involved too much RNG to succeed, I instead went for challenge #6. I went into this after finishing the campaign with a level 15 character (Kenji) wearing the Electric Jacket you can craft in the El Diablo islands.
In the beginning, craft the bow and precision rifle, but use only the bow on mobs - you'll want to save your rifle ammo for the end boss. Advance cautiously, taking on mobs as they appear, retreating when necessary. Always collect your arrows, and carve more out of sticks you can find. Make sure to pick up the flashlight on the way, it'll be dark before you'll reach the plane.
There are four encounters that deviate from standard distance zombie slaying:
1. A tapir will rush you after the buildings. Not too challenging if you know he'll be coming.
2. A zombie deer shortly before you reach the beach. If you played the campaign you'll know how to avoid getting hit.
3. The crabs on the beach. This will likely make or break your run. By the time you'll get here it will be dark, and will additionally have to keep an eye on night crawlers trying to rush you. There's not much to say except advance slowly and be extra vigilant, they got me twice.
4- The huge zombie boss at the end. Try to position yourself so he's barely on screen, then snipe him with the rifle. Don't forget about the mobs that trickle in.
If you take it slowly as you should, there'll be a storm during the beach sequence. But if you're wearing the Electric Jacket, lightning won't damage you.
Practice will make you perfect, and net the achievement. My winning run took about 15 minutes. In the process, you'll also unlock: