"hatch a plan" is correct and usable in written English.
You can use it when you want to talk about thinking of a plan or creating a plan. For example: "We need to hatch a plan to complete the project on time."
They began to hatch a plan.
The animals hatch a plan to trick the thieves.
Three of his friends agree to hatch a plan to escape.
At one point, some of the colonists hatch a plan to slaughter the native Indians.
Together they hatch a plan to "domesticate" the errant Lily Frankenstein.
Why hatch a plan to spread out starting assignments when Sabathia has been all but unhittable pitching every five days?
After getting reacquainted, they hatch a plan: to plant a bomb in police headquarters to destroy the incriminating film.
The characters hatch a plan by which Francis will get to kill Hannibal if Will sets him free.
The Simpson kids promptly hatch a plan to reunite Krusty with his dad (the voice of Jackie Mason).
Odds are, you heard someone hatch a plan to buy mansions and yachts as long as a city block.
So why would the Knicks hatch a plan that would not remove the bull's-eye from the back of No. 7's jersey, but enlarge it?
