In 1998, Ulybin earned the Grandmaster title awarded by Fédération Internationale des Échecs (FIDE), which is the international organization that connects the various national chess federations worldwide. Ulybin participated in numerous domestic and international tournaments, winning several of them.

One of his significant victories includes the Russian Championship (1997) for the Higher League. Internationally, he was the Champion of Russia and Israel in the festival "Evora-2000". He also played in the open chess tournament Cappelle-la-Grande (France) several times in between 1995 to 2013, securing a victory in 1997. Other notable achievements include his performance in the first European blitz championship in 2003 where he took third place.