Universal adversarial perturbation attacks are widely used to analyze image classifiers that employ convolutional neural networks. Nowadays, some attacks can deceive image- and video-quality metrics. So sustainability analysis of these metrics is important. Indeed, if an attack can confuse the metric, an attacker can easily increase quality scores. When developers of image- and video-algorithms can boost their scores through detached processing, algorithm comparisons are no longer fair. Inspired by the idea of universal adversarial perturbation for classifiers, we suggest a new method to attack differentiable no-reference quality metrics through universal perturbation. We applied this method to seven no-reference image- and video-quality metrics (PaQ-2-PiQ, Linearity, VSFA, MDTVSFA, KonCept512, Nima and SPAQ). For each one, we trained a universal perturbation that increases the respective scores. We also propose a method for assessing metric stability and identify the metrics that are the most vulnerable and the most resistant to our attack. The existence of successful universal perturbations appears to diminish the metric's ability to provide reliable scores. We therefore recommend our proposed method as an additional verification of metric reliability to complement traditional subjective tests and benchmarks.