What is the penalty for renting an apartment without taxes?

I cannot recommend you not to pay the filing fee, as this is against the legislation of Ukraine.

According to Art. 67 of the Constitution of Ukraine, everyone is obliged to pay taxes and fees in the manner and amounts established by the Law.

Every citizen who leases real estate (non-residential real estate, apartments, houses, rooms) for long-term or daily rent must pay personal income tax of 18 percent and 1.5 percent of the military levy on the income received.

Renting out an apartment without paying taxes is an offense punishable by a fine of 51,000 to 85,000 hryvnias (Article 212 of the Criminal Code of Ukraine).