UserCredentials credentials = new UserCredentials()
{
    Password = "<COGNITO USER POOL USER PASSWORD>",
    Username = "<COGNITO USER POOL USERNAME>"
};


CognitoIdentityProviderSettings settings = new CognitoIdentityProviderSettings()
{
     UserPoolID = "<USER POOL ID>",
     AppClientID = "<APP CLIENT ID>",
     IdentityPoolID = "<IDENTITY POOL ID>"
};

CognitoAdminAuthenticationProvider provider = new CognitoAdminAuthenticationProvider(settings);

var result = provider.Authenticate(credentials);

if (result.Challenge == null)
{
    var cred = provider.GetCredentials(result.Result);

    using (AmazonS3Client client = new AmazonS3Client(cred, settings.Region))
    {
        var listResult = client.ListBuckets();

        // Do Something.
    }
}