Davila, a native of Pomona, California, boxed with many of the best boxers of that division during that era. He challenged Carlos Zarate for the WBC's world title, losing by a knockout. Then , he beat Lupe Pintor by a ten round decision and lost to Wilfredo Gomez by a nine round knockout in Puerto Rico. When Pintor beat Zarate for the title, Davila was given a second chance in a rematch with the Mexican world champion, and lost by a fifteen round decision.
A few years later,during 1983, Pintor suffered a car accident and had to retire involuntarily, leaving the crown vacant, so the WBC assigned their number one challenger, undefeated Kiko Bejines, to box their number two challenger, Davila, for the title. The fight was held in Los Angeles, and it was described by sports writers as a rather tame bout. But Bejines held a slim lead on the judges' scorecards at the end of 11 rounds, and Davila, knowing that round twelve was the last round of the bout and it could also mean the last three minute chance of becoming a world champion he ever got, rushed out of his corner and attacked Bejines right away. With 21 seconds to go, a right hand to Bejines' chin struck, and when he fell to the floor, he struck his head against the ring's bottom rope. He was counted out and Davila began jumping all over the ring, having realized his lifelong dream of becoming a world champion. But then he heard the words from one of his trainers that made him feel as if a cube filled with ice had been dropped on his back: He was told Bejines was unconscious and being airlifted to a nearby hospital.
Davila spent the best part of the next three days by the side of Bejines' family at the medical center, until Bejines passed away.
He had to do some soul searching after that, and announced his retirement from boxing after the bout. However, there was one more fight under his contract with Don King and he had to comply. On the summer of 1984, he defended the title against Dominican Enrique Sanchez in Miami, in a fight in which Davila picked his shots carefully, perhaps worried that his punches might hurt his opponent badly once again. He was losing the fight on points halfway through it, but during round seven, rain started to fall and drenching the boxers and the whole open air arena. After that, it looked as if the rain had re-invigorated Davila, who ended up winning by an 11 round technical knockout.
Davila effectively retired after fulfilling that compromise with King, but money problems brought him back into the ring , and in 1987, he attempted to become a world champion again by travelling to Colombia and challenging Miguel Lora, but he lost a 12 round decision.
Davila now trains boxers in the LA area, but he has given numerous television talk show and newspaper interviews, where he has repeatedly declared that he wishes that his fight with Bejines had never happened.