Aftermath is a government park after a tsunami. There is seaweed and wreckage everywhere, and the main play space sits under a huge cargo ship which was deposited on top of a building during the storm. The area floods and quakes during gameplay, as the whole thing is teetering on the edge of falling into the water below. This has gameplay implications as it is difficult to aim during the quakes, and difficult to be stealthy while splashing through the water.
To get the Water Cleaver, you must be in a match of Horde (as this only works in Horde) and go to the "Statue" spawn. Go on the balcony nearest to the spawn and get to the top. Stand on the Longshot and turn around and look at the sky. You should see a flock of birds. Shoot and kill one of them and he'll explode like a Polyp. This may take a while. Once you kill one, head down the stairs inside the building directly below the clocktower and look off the ledge to the right from the bottom of the stairs. Keep looking until your screen starts to shake and you hear growling. Dodge to the back quickly as a Lambent Leviathan will try to smash you (it instantly kills you so be careful). When it submerges again, it drops the Water Cleaver on the ledge so go grab it. (Note: If you have Horde Command Pack or you're playing with a friend that does, all the command centers will spawn even on the bases you didn't buy.)