"Shirtlessly" (even if there was such a word) is an adverb modifying "climbed." One wonders how it is possible "to climb shirtlessly," or "to climb shirtFULLY" for that matter.
If what this cretin was trying to say was that the man was shirtless as he climbed, he might have said that "a shirtless, hammer-wielding man climbed ..."or some similar construction that actually used English the way it was intended.
>> One wonders how it is possible “to climb shirtlessly,”
No shirt!