Big tip for your enslaver killing adventures. If ever you get monster spawn boost by any means (ad boost video, Google play quests or purchasing), farm at floor 2 and constantly aim for enslavers only. It's the quickest way I've found to complete the feat. I completed the enslaver feat twice in a month because of that (took 3 hours and 30 dq minutes). Even in 5 mins you can get 5 pets saved or 6. Eternal pets will be rare though but just keep on farming hard. I only learnt that recently.
Yes pets are effected by luck so the higher the luck, the higher chance of legend pets (I gained 5 in a row to kill 2 enslavers plus a few extra).
Higher eternalized will help (eternalised 6 replacing Nadroji set affix for eg). I did luckily get an eternal pet called spike though but it's not as impressive affixes.The real challenge is getting a good eternal pet but getting a good legend pet is a better priority as it's slightly easier.
Just keep on farming until you get something you want is all we can say. More hours of course helps if you have the time to spend but that's up to you.