"Adventure" can mean "excitement" as in "His life is filled with adventure." Or it can be something more specific as in "He is back from his latest adventure in Sweden." What does "äventyr" mean here AND can this sentence be translated as both "I am tired of adventure/adventures"?
My translation was: "I am weary from adventure", trying to imply there were some adventures that I did, and now I am feeling physically tired at this moment (and this translation was marked incorrect).
For that case, one would use your "Jag blev trött av äventyret"?
Does the original "Jag är trött på äventyr" only mean that I am generally done with adventures / want no more adventure... or can that sentence also have the 'physically tired right now' meaning as well?
Yes, the original sentence only means you're done with adventures, not that you're exhausted right now. If you want to say 'weary from adventure' you'd have to go with, as you said, jag blev trött av äventyret or you could say … alla äventyr – the thing that made you tired has to be definite somehow, it doesn't really sound natural with just äventyr: