I was wondering if this sentence is correct:
She tried to serve the poor at any whatever cost.
I think it should be either:
She tried to serve the poor at any cost.
She tried to serve the poor at whatever cost.
However, a university used "at any whatever cost" on their entrance exam.
You are right the sentence is unacceptable.
I prefer the first of your alternatives.
The second might be better as -
She tried to serve the poor whatever the cost.