Replacing the blank with who or whom, would imply that Mount Everest is a person. So, this means both who and whom is incorrect.
Replacing the blank with that would be grammatically incorrect. So, this means the word 'that' would be incorrect.
This leaves us with the remaining option of 'which'.
The word 'which' would be grammatically correct for this sentence.
The final, correct sentence should something like this:
Mount Everest, which is the tallest mountain in the world, has provided a challenging adventure for many climbers.