Gentleman, you can never give up at any one time even you are in difficult situation when killing those zombies! Survival is the key to success!. The master of survival is the only winner here.
Survive as human in Zombie Modes (1, 2, 3, 4).
[Evolutionist]
An evolution is the truth. A best zombie player who conducts continuous evolution.
Evolute as a Zombie 10000 times.
These also the Zombie PvP modes but with some different goals:
Soldier, I've heard that no one is ever close to your escape ability. Show me your skills and ensure that the following zombies at the back are not a worried to you. Available to achieve in above 4 people room.
Escape 3000 times in Zombie Escape mode.
[Infecter]
Gentleman, sometimes we have to betray our team and work with the enemy to survive. How about you? Are you cold enough to go against your comrade of yesterday? Note: At least 8 players in a game.
Infect 5000 humans in Zombie Escape mode.
[Bot Zombie Master]
Gentleman, you shouldn't belittle on them just because they are dead. Don't forget they are zombies.
Unlock Difficulty Level, 'Elite', in Bot Zombie Mod.
However, there are several modes that are categorized as Zombie PvE mode (Player vs Environment):
Gentleman, you must utilize your ability to survive from the dead city. Don't forget that you can only protect you and your comrades by collecting, building, and fighting. This can only be achieved in rooms with 4 players.
Clear New Zombie Shelter: Co-op for 100 times.
[Destroyer]
Gentleman, what will you do to survive with limited resource? You must protect your own resource and steal other people's resource. You can only survive by destroying the enemies in the world. This can only be achieved in rooms with 6 or more players.
Achieve 100 victories in New Zombie Shelter: Team Match.
[Asura]
None
Finish Zombie Scenario season 1 to 3 in order.
Trivia
A common bug which players may find is when a zombie instant kills another one upon infecting him, this may happen only if a host zombie infects someone.
Humans infected by origin zombies will receive a very high amount of health power, resulting sometimes higher than when evolving into an origin zombie which has 7000 health. Therefore your hp will be reduced if you had more than that.