From the Super Mario Wiki
The Big Berthas ("Kyodai Pukupuku ♀" in Japan) are huge Cheep Cheep that live deep in the sea. All Big Berthas seem to be mother fish, as she always carries Baby Cheeps in her mouth, occasionally letting them out. After a few seconds, the Baby Cheep will return to its mother's mouth. Her male counterpart, Boss Bass, is an aggressive hunter that swims on the surface, never seen in deep water.
Super Mario Bros. 3Super Mario Bros. 3. Unlike the aggressive hunting Boss Bass, this gender of the creature is more gentle and nests comfortably underwater. If Mario or Luigi swims in her way, she may passively eat him (unless he's in frog form).
The Adventures of Super Mario Bros. 3
It is possible that Big Berthas made appearances on The Adventures of Super Mario Bros. 3. However, they were never seen with Baby Cheeps, usually chased after the good guys, and were never referred to by name. Whether these fish were supposed to be either Big Berthas or Boss Basses is unknown. They prey on others, but are often seen in deep water.
Nintendo Comics System
Big Bertha also played a prominent role in the Nintendo Comics System. In her first appearance, Love Flounders, she falls in love with Mario in a Frog Suit after being tricked by Stanley the Talking Fish. She eventually realizes Stanley was lying, but is consoled by Mario, who states he wants to be friends with Bertha, not lovers. Big Bertha later reappears in Fins and Roses, this time dating Stanley. She foils Wendy O. Koopa's plans by knocking the Koopa's bomb back at her.
Super Mario 64 DS
In Super Mario 64 DS, Big Berthas do not spit out Baby Cheeps, and replace Bubba from Super Mario 64. Like the Bubbas from the original game, they will aim in on Yoshi, Mario, Luigi, or Wario, mouth wide open, attempting to eat them. If a character is eaten, that character will lose a life, regardless on their current health. Also, the first Big Bertha can be defeated with a nearby Super Mushroom. In this game, it resembles a Cheep Chomp.
Yoshi's Island DS
It is probable that Bessie Bass, one of the bosses from Yoshi's Island DS, despite having the word "bass" in her name, is actually a Big Bertha, since she is female (the "bass" in her name merely denotes that she is of the large red bass species that Boss Basses and Big Berthas are members of).