give an arm and a leg (for something)
To pay, give, or do whatever is necessary or required. They had to give an arm and a leg for the lawyer they hired. I had to give an arm and a leg just to get an interview for the job.
give an arm and a leg for something
If you say that you would give an arm and a leg for something or to do something, you mean that you want it very much. I'd give an arm and a leg for a cup of tea. Any jazz professional would give an arm and a leg for half an hour playing with Wynton Marsalis.