Limon is very famous also for his legendary rivalry with Bobby Chacon. Their first fight took place on December 7 of 1975, in Mexicali, Mexico. Limon defeated Chacon by a decision in ten that day.
It was around 1977 and 1978, that negotiations took place to put Limon against the WBA's world Jr. Lightweight champion, Samuel Serrano. However, the negotiations stalled and that fight never took place.
After Limon unsuccessfully challenged Alexis Arguello in February of 1979, (losing by a knockout in 11 rounds for the WBC's world Jr. Lightweight title) he and Chacon met for the second time. That time, the fight ended in a seven round no contest. Limon and Chacon met for the third time on March 21 of 1980, in Los Angeles. Chacon came out the winner, by a decision in ten.
Despite losing his third bout to Chacon, it was Limon who later that year found himself fighting for the world title that Arguello had vacated. And so, Limon became the WBC's world Jr. Lightweight champion by knocking out Venezuela's Idelphonso Bethelmy in round 15 at Los Angeles.
Before his first defense, against England based Ugandan Cornelius Boza-Edwards, Limon made a tragic reference to the fight between Lupe Pintor and Johnny Owens, which had taken place the year before, and after which Owens died. His comments shocked many, because he suggested that Boza-Edwards should expect something tragic to happen since this was another bout between a Mexican and a fighter with British connections. Boza-Edwards nevertheless, went on to become world champion by beating Limon by a 15 round decision.
In 1982, Rolando Navarette was the WBC world Jr. Lightweight champion, after dethroning Boza-Edwards. Limon was given a chance to recover his title, and he became a two time world champion by knocking Navarette out in round 12. After defending his title successfully once, Limon once again met Chacon. Their fourth bout, held on December 11 of 1982 in Sacramento, was the first bout in their series with a world championship involved. Lmon dropped Chacon in round three, but was subsequently dropped in round 10, and with a few seconds left in round 15. Chacon won the fight by a split decision. The fight won various Fight of The Year awards for 1982.
In 1983, Chacon refused to defend his world title against Hector 'Macho' Camacho, so Limon accepted the opportunity to travel to Puerto Rico to try to become a world champion for the third time. This time, however, he was knocked out in five rounds.
Limon went on boxing until the 1990s, but he never again challenged for a world title. He did fight, however, a number of world champions and important boxers from 1984 to 1992, including Julio Cesar Chavez and Roger Mayweather, both of which beat Limon.
Limon's exact record is unknown, but it is thought to be around 55 wins, 18 losses and 1 no-contest, with around 37 wins by knockout.