How can I skip the rat shooting level in Theme Hospital?
Blade Wraith's answer is misleading. There is no way to go back to the "level select" screen (which isn't even a selection screen).
You will need to leave the game running. The rat challenge is designed so that you extend the time you get by killing rats (which the handymen need to clean). As long as you don't engage with it, it doesn't take very long (5-10 minutes at most).
You could also try changing the game speed to And Then Some More, making it go even faster, though some versions may disable this.