Rain relies heavily on its primary rain setter. Killing that early makes it a lot more difficult for your opponent to set up on you. However, a good rain will always have other methods to set up rain, such as klefki, or thundurus. This means that to prevent them from setting up rain, you have to maintain a constant pressure when those pokemon are in, so that either they chicken out of setting up, or they set up, and die. As for what happens after rain is up, the majority of rain-induced set-up sweepers rely on a powerful water STAB move, so it's great to have a reliable bulky water type which can come in and either wall them, or stall the rain out. The turn their rain runs out is the turn their team is at its weakest, and that is the best time to break it.