Basic Trope: A character sends out a monster to defeat another monster.
Straight: Bob sends his crazy brother Jim to save Alice from a madman.
Exaggerated: Bob takes Jim, makes him a Power Ranger, puts him in a Megazord and then sends him to save Alice from a madman.
Downplayed: Bob sends out his dog to quiet down his neighbor's dog.
The only one left who can fight the monster at all is a monster itself.
The "bigger fish" was specifically made for dealing with the smaller fish in question.
Jim is sent against Bob by a madman who's holding Alice captive.
Bob is sent against a madman by Jim who's holding Alice captive.
Subverted: The madman gets a hold on Jim and then sends him after Bob.
Double Subverted: ...And then Bob convinces Jim that he should be after the madman.
Parodied: Whenever the protagonists are faced with a big monster they can't defeat, they cast their magical Even Bigger Monster spell, or call the Bigger Monsters For Hire company.
Zig Zagged: ???
Averted: Jim doesn't fulfil his mission.
Lampshaded: When Bob points out that sending Jim in was just summoning a bigger fish.
Invoked: Bob specifically takes Jim from the mental institution.
Exploited: Bob then uses Jim for many things requiring a handy crazy person.
Defied: Bob doesn't call his brother (and phones the police instead).
Discussed: Bob talks with his friends about how would he deal with a madman kidnapping Alice, and mentions his crazy brother.
Conversed: Bob talks with his friends about a situation where the protagonist of a Show Within a Show summoned a "bigger fish".
Deconstructed: The heroes Summon A Bigger Fish to take out the creature rampaging around town. The new monster wins... leaving the heroes to realize that the monster they just summoned will be just as devastating as the original one was.
Reconstructed: The summoners expected this, and included a way to un-summon the bigger fish once it wins.
Plotted A Good Waste: When Bob intends to call the police, but ends up calling Jim instead.
Played For Laughs: Bob calls Jim, but Jim wants to do something completely different. Hilarity Ensues.
Played For Drama: Bob calls Jim. Jim is now determined to find Alice and the madman, get her and probably also do something with the madman.