this thread has a good discussion on the subject, and @Mr_Scooty added an update for 3.0 later in the thread.
in the Feats section of the Codex, on floor 400+, you can kill Enslavers until you get the Mythic Enslaver which drops a random Eternal Pet.
if you Craft an Eternal Pet Farming Build and farm on floor 400+, you increase your chances a little bit of the Enslavers dropping an Eternal Pet.
from what I understand, Enslavers usually drop a Normal, Magic, Rare, or Epic Pet. with high Luck, you get better chances of Rare & Epic Pets, with a small chance for Legend Pets. when you complete the Enslaver Feat, it drops a Legend Pet Reward. any Legend Pet drop has a 1% chance to drop as an Eternal Pet.
if you’re using the monster spawn boost, then spam farm the lowest floor (21?) with an Eternal Pet Farm Build. the Pet will be low level, but you can increase it’s level by killing monsters for experience.