• Armed civilians without giving them a uniform. Breach of Geneva Conventions
• Ukrainian special forces command said Russian artillerymen will no longer be taken prisoner and will "all be killed for being complicit in criminal orders". Killing surrendering soldiers is a war crime. Collective punishment is also one. Edit: they have since taken that statement back. I have not.
• Did not activate air raid sirens to warn civilian populations of artillery and air strikes. People have already died because of this; Russia gave warnings as per protocol which Ukraine did not relay in time.
• As per the discovery of biological labs near the border with Russia, there is a very serious possibility Zelensky is guilty of producing biological weapons. The labs have been confirmed by the US gov, but no proof yet that they were meant for biological warfare.
• Forcing battles to happen in civilian zones, thus exposing them to danger and preventing their protection.
• Possibility of using child soldiers, as the Ukrainian army is now training children to use AKs, during wartime.
• Ukrainian forces were (accidentally) caught using Red Cross vans to transport soldiers and materiel. The symbol of the cross itself can only be used by the organisation and is protected under the Geneva Conventions; it can only be used by medical units who must then be treated like civilians.

Feel free to contribute. (the list above only reflects crimes Zelensky himself can be responsible for, to the best of our knowledge based on information that comes out of Ukraine. This list is also not legal advice, as only a trial will be able to determine which crimes have been committed and who is responsible for them).