I managed to get through all 10 levels of District 1 all by myself by :
1) sticking with decent weapons when they were given to me, and ignoring all subsequent weapon drops. This meant that I had a guided missile launcher and a machine gun.. I also picked up all other drops/perked that were given me. But I did not pick up other weapons. I stuck with what I was given at about level 5.
2) positioning myself in a corner of the map which meant that llamas could only approach from 2 sides (instead of 4). I could retreat into the corner, and focus fire in a smaller area when the llamas approached, and ventured out gingerly only when the coast was clear.
3) Shooting vehicles thus blowing them up taking llamas with them.
4) on the levels with nests, head straight for them and deliver furious anger via hail of ammo and jumping on them etc..
i.e. get rid of them before they dispense hordes of llamas.
I found that the last 4 or 5 levels I had about 6 bars on my health meter, and did not lose any at all until the final 10th level, whereupon
The 10th level is
*** Spoiler - click to reveal *** in the sewers, then a scientific facility, whereby you follow a corridor and there is a much larger volume of llamas to face. I went down to about 2 bars of health here due to backtracking unnecessarily and because of the larger volume of llamas in the 10th level. Continue on the route through the facility and you get to the last room.
Done! Hurray!