What part of speech is the word up cat climbed ladder right behind me.?

That's not a word, but a sentence! Here's how to break it down by parts of speech:

* Up - Adverb (modifying the verb "climbed")

* Cat - Noun (subject of the verb "climbed")

* Climbed - Verb (past tense, describing the action of the cat)

* Ladder - Noun (object of the verb "climbed")

* Right - Adverb (modifying the prepositional phrase "behind me")

* Behind - Preposition (showing the relationship between the cat and "me")

* Me - Pronoun (object of the preposition "behind")