Biggs' first major success as an amateur boxer was winning the gold medal at the 1981 United States National Boxing Championships in the super-heavyweight division. He repeated this feat the next year, and also in 1982 he won the World Championships in Munich, West Germany, where in the final he defeated Francesco Damiani from Italy on points, who beat the legendary Teofilo Stevenson earlier in the competition. In 1983 Biggs won a bronze medal on the Pan American Games, losing to future professional challenger Jorge Luis Gonzalez in the semi-final. In addition, Biggs won a 3–2 split decision over Cuban Angel Milian, who had beaten Greg Page five years earlier.