On what basis did Aristotle classify different animals?
Aristotle classified animals (and plants) and humans based on their soul, way of life, actions, and physical attributes.
Aristotle's most lasting classification was based on physical attributes and those with similar characteristics where put into genera and then differentiated by species. We still use part of this classification system today.
First he divided animals based on blood; those with or without red blood. This closely aligns with our modern division between vertebrates and invertebrates.
Those with blood (vertebrates) where then divided into viviparous quadrupeds (mammals), birds, oviparous quadrupeds (reptiles and amphibians), fishes, and whales. Non-blooded (invertebrates) were divided in cephalopods, crustaceans, insects, and shelled animals.
Our current classifications and standards have shifted somewhat over the years since Aristotle considering that Aristotle included spiders in his insects although we now call them arachnids. We also now know that whales are mammals and include them as such. However, Aristotle's original classification system lasted for many centuries as the ultimate classification system. It also served as the basis for our current system.