I found "A sledgehammer to crack a nut" as one example. What are some others?
Consider "to break a butterfly on a wheel":
Who breaks a butterfly upon a wheel?
A rhetorical question referring to an excessive amount of force that has been applied to achieve something minor, unimportant, or insignificant.
To "break upon a wheel" refers to a mode of torture, in which a victim has his or her bones broken while strapped to a large wheel.
If a single word is OK, try overkill:
An excess of what is necessary or appropriate for a particular end
Also, you can use a sledgehammer to swat a fly, too.
Shoot a rabbit with an elephant gun (also kill a fly with an elephant gun), meaning to do something with excessive force, or to find a massively overpowered solution to a minor problem.
This was apparently referenced in a line of dialogue from a 1951 Bugs Bunny cartoon, although whether it created the idiom or just used it is unclear.
"To bring a gun to a fistfight." With the reverse sense of "To bring a knife to a gunfight."