Once you get past level 11 of Breakdown, the game doesn't appear to get any harder. Possibly spawn rates go up, but the numbers behind damage and health do not change. At this point, you need to learn what to bring with you when you leave your base in order to have the best chance of survival. Especially when your characters are 1 stars! They feel like sitting ducks when you first play at high levels with these new recruits, but soon you'll turn the odds in your favor.
The one thing you have going for you at later levels is a plethora of items. Personally I have a game going right now with 100+ suppressors, 500+ firecrackers, 250+ steel pipe bombs, 1000+ assorted meds, 1250+ firebombs, etc. So you can use this kind of stockpile to your advantage, especially with the newer members of your team. If you're using my Level 30 Breakdown Strategy, then you're going to end up spending the majority of your game time playing people outside of your six man team.
Slot #1: Bring a Gun
Always bring a gun for killing bloaters and screamers at range. DO NOT use firebombs on the bloaters because they will eventually let out a super loud explosion. What kind of gun should you use? If your only goal is to kill bloaters and screamers then you'll want a high capacity pistol with a suppressor. For now, let's start with that. I'll have to cover killing specials in a separate post.
Slot #2: Heavy or Blunt Weapon
If you're playing a new character then I recommend the heavy or blunt weapons. When going with a heavy weapon, use something like a wood axe (the best) or hockey stick because they are light weight. Trying to use an edged weapon can quickly become a disaster because it's hard to predict when you'll actually kill the zombie. Plus the alternative melee weapons enable you to hit multiple targets per swing. Remember to use big swings (Hold L1 while attacking) on solo targets to dispatch them quickly. After the first big attack, follow up with quick regular attacks to stagger your opponent faster. Doing big attacks in a row is too slow, so the zombie resets to a standing position before each swing usually.
Slot #3: Food
This is even more important than remembering medicine. What sucks right now is that the game won't let you keep more than 6 food after each simulation! You actually create the food each time, as it's reset to 0, so you can end up with 2-4 food as well. Sucky I know, but we must survive this apocalypse no matter how unfair things become. Bring 2-3 food on your character and be sure to use it BEFORE you get into trouble.
Slot #4: Medicine
Rarely do I ever play under 100% health at the higher levels, so I pop 6 influence medicines like crazy. Bring 3 with you and use frequently.
Slot #5: Firecrackers (Optional)
Those four items are the keys to staying alive, but they don't cover every danger that's out there. For example, getting surprised by large hordes of zombies usually means death for our lowly one star fighters. Therefore, it's wise to pack a few firecrackers to get away. Firecrackers are vastly superior to every other noise maker, so create them frequently from any workshop.
Slot #6: Steel Pipe Bombs (Optional)
You can substitute any explosive for these if you haven't started making them yet. Since they take so long to craft, I highly recommend playing a level at snyders and building four munition shops to crank them out super fast. Why do you need them? For infestations and big uns. Even your super crappy level 1 characters can destroy infestations with one steel pipe bomb and big uns with two blasts. These bombs are surprisingly quiet as well.