Introduction: The COVID-19 pandemic has affected the mental health of the population. This study aims to assess the prevalence of subjective depressive and anxiety symptoms as well as assess the quality of life in different waves of the COVID-19 pandemic based on an online survey. Methods: The study was conducted based on an original and anonymous questionnaire, consisting of a section assessing sociodemographic status and psychometric tools: Beck Depression Inventory (BDI), Generalised Anxiety Disorder Assessment (GAD-7) and Manchester Short Assessment of Quality of Life (MANSA). A total of 6739 people participated in the survey, with the largest number from the first wave of the pandemic (2467—36.6%), followed by 1627 (24.1%) for the second wave, 1696 (25.2%) for wave three and 949 (14.1%) for wave four. The mean age of the study group was 28.19 ± 9.94. Results: There was an initial, gradual increase in depressive and anxiety symptoms over the three waves. There were no significant differences in the quality-of-life scores, except for the second and third waves (−0.0846; p = 0.013. It was found that women, residents of big cities and people with psychiatric history showed higher BDI and GAD-7 scores. Conclusions: The impact of the pandemic on mental health was not homogeneous, with the first three waves of the COVID-19 pandemic having more of an impact compared to the fourth wave. Female respondents’ sex, history of mental disease and reduced earning capacity exacerbated psychiatric symptoms.