Aleksandr Batyuk made his international début at the 1980 European Junior Championships, where he won gold in the relay and bronze in the 15 km. Batyuk won all his next international championships medals in the relay, including a gold at the 1982 World Championships, and a silver at the 1987 World Championships. He also was fourth and fifth in the 50 km and 15 km, respectively, at the 1982 World Championships and also took part of the 1987 World Championships, where he was eighth in the 15 km. Batyuk made his last international appearance at the 1988 Olympics, where he placed 15th in the 15 km. Domestically Batyuk won one individual Soviet title in the 15 km in 1985 and one relay title in 1983. After his sporting career Batyuk worked as a cross-country skiing coach in his native Ukraine, later becoming the head coach of the Ukrainian national cross-country team. His son Oleksandr Batiuk also became a cross-country skier, who later switched to biathlon, but competed at the 2006 Olympics in cross-country skiing representing Ukraine.