The words given are the meanings of Greek roots or in some cases Latin roots. These roots can be combined to make words of the given lengths. There's some ambiguity about what the actual roots are and what combines with what, which could be somewhat of an obstruction for solvers. Multiple meanings are often given to hopefully help a bit with this ambiguity.
The only possibility that explains all the words and matches the given lengths below, however, is that the words are hierarchy (sacred + rule), biology (life + study), vituperate (fault + provide, both Latin), hypersphere (beyond + ball), and tricycle (three + wheel, both arguably Greek and arguably Latin).
Taking the boxed letters from these words gives us:
_ _ _ r _ _ _ h _This spells out, reading first the first letters and then the second letters, "river horse", which is a clue for the answer.
Answer: hippopotamus