Zatonskih won many Ukrainian girls' titles in several age categories. In 1999 she was awarded the WGM title by FIDE. She won the Ukrainian Women's Championship in 2001. She represented Ukraine in two Women's Chess Olympiads, at Istanbul 2000 at Bled 2002, and in two Women's European Team Championships, Batumi 1999 (where she won a silver medal on her board) and Leon 2001.