As a linguist, this is how I would parse the sentence:
Christopher - proper noun
the - determiner, more specifically, definite article
fantastic - adjective
zookeeper - noun
left - verb, past tense
his - possessive pronoun
unbelievable - adjective
book - noun
on - preposition
the - as above
bed - noun
THE BASIC ANSWER:
Adverbs are words that modify the verb in a sentence. Typically, they are words that end in '-ly' such as 'quickly', 'ambitiously' (and 'typically', ho ho), etc - but note that some common words that don't follow this form are adverbs, like 'too', 'almost', 'afterwards' and 'often'.
Now the only verb in this sentence is 'left' (past tense of 'to leave'), and I can see no words modifying it.
THE EXPLANATION OF THE BASIC ANSWER:
Allow me to go into more detail:
The sentence follows the pattern Subject - Verb - Object. The Subject is 'Christopher the fantastic zookeeper' - with the latter phrase modifying 'Christopher, not the verb. Then we have our Verb, 'left', followed by 'his unbelievable book', which is the Object. This fills in the compulsory gap after the Subject and Verb, answering the question 'what did Christopher leave' - but crucially not HOW Christopher left if. That is what an adverb does, so this phrase cannot be it. The final prepositional phrase 'on the bed' is telling us something about the book, so this cannot be modifying the Verb.
So your simple answer is that there is no adverb in the sentence. But...
THE DIFFICULT ANSWER:
After all that - if you've followed me - the thing about adverbs is that they're slimy creatures, hard to pin down. They can also be defined as words or phrases that modify ANY other part of language, not just verbs but also adjectives, clauses and sentences (note that words modifying nouns are not included - these are adjectives or determiners).
By this more broad definition, one could say that the prepositional phrase 'on the bed' is an adverb (or rather, adverbial phrase), because it is modifying the whole sentence.
So which answer you choose depends on what you need the answer for. If you're a pedant settling a score, you can choose the answer that suits your case - I'm not taking sides! If you're a school kid, I doubt you'd be expected to go into that much depth - if in doubt just look up each word in a dictionary and it will tell you what part of speech it is. If you're writing a detailed undergrad essay about adverbs, you probably should go into this depth and more - but you should probably also read your Ling 101 textbook first :-)
BA Linguistics (First) Lancaster University, UK
MSc Linguistics (ongoing) University of Edinburgh, UK