The phrase 'costly endeavor' is correct and usable in written English. You can use it to refer to an effort, task, or activity that is likely to be expensive to complete. For example, "Financing a college education can be a costly endeavor.".
In any event, naming is a costly endeavor.
Designing and building things for the United States military is a notoriously slow-moving and costly endeavor.
Historic restoration, they point out, is a costly endeavor, something that many elected officials failed to appreciate.
They went to her opponents -- incumbent lawmakers -- and with that support came party volunteers to carry nominating petitions, a costly endeavor, Ms. Gotbaum learned.
To pay for similar research in the much larger Pacific Ocean, he turned to crowdfunding the increasingly popular method of using the Internet to bring multiple people together to fund costly endeavors.
Clinical trials for preventative therapies are complex and costly endeavors focused on individuals likely to develop disease in a short time frame, randomizing them to treatment groups, and following them over time.
It wages these costly endeavors with the price of oil at historic lows.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union