The show also featured the first of three Lucha de Apuestas, mask vs. mask match series for the Triplemanía III shows as the culmination of a storyline feud between the tecnico team (faces, those that portray the good guys) of Super Caló and Winners against the Rudo (heels, those that portray the bad guys) team known as Los Diabolicos ("The Diabolical Ones"; Ángel Mortal and Marabunta).

The Triplemanía show featured seven professional wrestling matches with different wrestlers involved in pre-existing scripted feuds, plots and storylines.

Initial plans for the 1995 Triplemanía III series of events included a storyline where Los Gringos Locos members Eddy Guerrero and Art Barr would turn on teammate Konnan in the fall of 1994.

This was supposed to turn técnico and set up a Lucha de Apuestas, or bet match, between Konnan and Art Barr where both would put their hair on the line.

[6] Barr's death, coupled with the Mexican peso crisis in 1994 led to Guerrero leaving AAA to work in the United States instead and thus made a Los Gringos Locos storyline impossible to piece together.

At one point Máscara Año 2000 broke a glass beer bottle over Aguayo's head, causing him to bleed so badly that he had to be taken from the arena on a stretcher.

When Peña left CMLL to form AAA he made sure the Mini-Estrellas were given a strong presence on the shows and for Triplemanía III-A they were actually given the main event slot.

The basic storyline centered around two the "veteran" wrestlers in Los Diabolicos getting annoyed with the fan reaction Super Caló and Winners were getting without, in their opinion, earning it by proving themselves in the ring.

Peña turned Jesus Andrade, previously known as Espanto Jr. into the masked "Pentagón" character, a rival and distorted mirror image of Octagón.

On November 6, 1994 then-Mexican National Light Heavyweight Champion La Parka teamed up with Jerry Estrada and Blue Panther, losing to a team of international wrestling stars The Pegasus Kid, 2 Cold Scorpio, and Tito Santana as part of the AAA When Worlds Collide pay-per-view (PPV).

[15] On March 28, 1995 Estrada won the championship from La Parka in a high profile match in Matamoros, Tamaulipas as part of the long running storyline between the two.

[16] For Triplemanía III-A the two found themselves on opposite sides of each other in an eight-man "Atómicos" tag team match that paired up four high profile feuds of the time between Konnan and Cien Caras, Perro Aguayo and Máscara Año 2000, La Parka and Jerry Estrada and finally Octagón and Pentagón to complete the two sides.

Following the match Ángel Mortal tried to escape the arena but was forced back in the ring where he was unmasked and revealed that his real name was Juan Manuel de la Rosa.

[8] In the semi-main event four different storylines intersected in an eight-man "Atómicos" tag team match featuring the top feuds of AAA at the time.

[24] Super Muñequito would later lose the Mexican National Mini-Estrella Championship to Espectrito I as part of their long running rivalry.

In the end Cien Caras and Máscara Año 2000 retained their championships when Perro Aguayo was disqualified in the third and final fall of the match.

[24] Konnan would later on move to World Championship Wrestling (WCW) and work in the United States for years, putting an end to his rivalry with Cien Caras.

Aguayo's rivalry with Cien Caras and Máscara Año 2000 would carry on for years, even beyond Aguayo's initial retirement from wrestling as Cien Caras and Máscara Año 2000 brought him back for one more Luchas de Apuestas match as part of CMLL's 2006 Homenaje a Dos Leyendas show.

[24][29] On August 6, 1995 La Parka regained the Mexican National Light Heavyweight Championship from Jerry Estrada as their feud continued into 1996.

[32] AAA originally intended to carry the storyline forward into the next "generation" as they introduced Octagón Jr. in 2012 as well as a character supposed to be his rival in Pentagón Jr.

The storyline between the team of Winners/Super Caló and Los Diabolicos led to Winners and Marabunta facing off in a Lucha de Apuestas match at the subsequent Triplemanía III-B on June 18, 1995.

In the end Super Caló won, forcing Winners to unmask and reveal his real name, Andrés Alejandro Palomeque González.

[21][36] John Molinario, who writes about wrestling for the Canadian Online Explorer, called the three "an outstanding TripleMania series" when reviewing the first five years of Triplemanía in a 2000 article.