Under what ruler did the Aztecs reach their greatest power?

The answer to this is not clear-cut, as it depends how you define 'greatest power'. Nevertheless, we could say that the Aztec empire was at it's largest just before the Spanish conquest. Ahuitzotl was the eighth Aztec ruler, and under his reign (from 1486 to 1502), he more than doubled the area of land controlled by the Aztecs. His successor, Moctezuma II also made substantial land gains and, in fact, the empire reached it's maximal size under his rule. Moctezuma's rain is, however, coloured by his defeat at the hands of the Spanish, and is therefore not generally regarded as the greatest Aztec ruler.