Testing for exceptions in async methods

You should use Func<Task> instead of Action:

[Test]
public void TestFail()
{
    Func<Task> f = async () => { await Fail(); };
    f.ShouldThrow<Exception>();            
}

That will call the following extension which is used to verify asynchronous methods

public static ExceptionAssertions<TException> ShouldThrow<TException>(
    this Func<Task> asyncAction, string because = "", params object[] becauseArgs)
        where TException : Exception        

Internally this method will run task returned by Func and wait for it. Something like

try
{
    Task.Run(asyncAction).Wait();
}
catch (Exception exception)
{
    // get actual exception if it wrapped in AggregateException
}

Note that test itself is synchronous.