The correct answers are He was completely out of breath because he had been running from the police. and His boots were covered in mud because he had been walking through the marsh.

The past perfect continuous (had been + verb-ing) is used to describe an ongoing action in the past that caused a visible result later in the past (like being out of breath or having muddy boots).

"Has been hiding" is present perfect continuous, which doesn't fit a past story. "Had been run" is grammatically incorrect; it should be "had been running."