Good one...
OK, first the striaght-up answer: This is an adverbial phrase with a prepositional complement using a "fossilized accusative" (erstarrter Akkusativ).
Now the long answer: The prepositional complement is "um den Willen" (around/about the will) wit the genitive object "des Himmels" (of heaven), coming together as "Um den Willen des Himmels" (About the will of heaven ==> for heaven's sake). In a process called "grammaticalization" this morphed into "um Himmels willen", whereby the "um ... willen" forms a circumposition (like "um ... zu"), in which the noun "Wille" turned into it accusative form "Willen" and became the postpositional part of the circumpositon as a "errstarter Akkusative" in the lower case "willen".
Alle Klarheiten restlos beseitigt? (Was all clarity removed without trace?) ... ;)
HTH
Armin