Final answer:
Animal life underwent its greatest diversification during the Cambrian period of the Paleozoic Era, which began about 544 million years ago.
Step-by-step explanation:
The greatest diversification of animal life occurred during the Cambrian period of the Paleozoic Era, which began about 544 million years ago. This period saw the emergence of a vast array of animal phyla and is known as the Cambrian explosion.