Updated Eternal Pet Thread for Version 3.0 → Better Late than never.
3 New Feats for 3.0 for Enslavers
Slay Enslavers - Kill 50 Epic (orange) Enslavers above map floor 400 to Spawn 1 Legend Enslaver
Slay Legend Enslavers - Kill 10 Legend (red) Enslavers above map floor 400 to Spawn 1 mythic Enslaver.
Slay Mythic Enslavers - Kill Mythic (purple) Enslavers for 100% Eternal Pet drop above map floor 400. Slaying a Mythic Enslaver will guarantee an Eternal pet → here is some luck from me to you in obtaining the best pet possible. 
The new Enslaver feats are in addition to the previous Slay Enslaver feat where a Legend Pet will drop after 200 Enslaver kills (not accounting for Accomplished Ascension or kill 150 for Legend Pet).
Recommendations below for quickly obtaining eternal pet(s).
1. Eternalized set. I use 2 eternalized gears.
2. Treasured ascension for 300% increased eternal chance.
3. Fortunate ascension for 200% additional luck.
4. Epiphany set to go 25% above cap.
5. Monster spawn boost $0.99 for 1 hour guarantee of every map containing an Enslaver.
You can also not spend any money and you can use Google Opinion Rewards for equivalent In App Purchases. Also, look further down in the message chain (Link below) to see where you can make the google app work even if it is not available in your country – many thanks to @TYRON for providing a great workaround.
6. Speed - you need to be fast. Either max move speed, teleport / shatter, vault, charge etc. You should be able to locate the enslaver quickly via list provided above.
7. Luck @1012% & Eternal find rate/chance 600%.
8. Instant kill ability.
9. Accomplished ascension for 25% feat reduction. Makes enslaver feat 150 instead of 200. This also reduces the new Enslaver Feats for 3.0 from 50 Epic to 38 to Spawn Legend and from 10 Legend to 8 to Spawn Mythic Enslaver.
10. You do not have to play on Mythic 3 difficulty map. You should try lower difficulty (Easy, Epic, Legend, Mythic 1 or 2) maps as long as your luck is still 1012% (accounting for Epiphany from item 4 above). You can also play Floor 2 of any map difficulty but when you sell gear, you will not receive much gold and when you convert gear, you will go bankrupt quickly. Playing floor 2 will also give you no credit towards the new Enslaver feats.
11. Since Version 2.5, I use Double Nadroji Bonus from the Chest and Helmet gears during normal gameplay. Equipping 2x Nadroji Bonus gives 200% enemy rarity (you can check your Adventurer stats page to visually see this cool effect). I cannot definitively tell you this ~Will~ increase your odds of encountering an Enslaver. However, based on my tests with Double Nadroji Bonuses equipped and not equipped, I could tell a difference in the amount Enslavers that spawned.
With changes to Version 3.0, play at Floor 401+ on any difficulty so are able to take advantage of the new Enslaver feats. With monster spawn boost, I am typically able to find and kill enslaver between 10-30 seconds. You can buy a challenge map on whichever Difficulty you want to play and convert the map until it is at least Floor 401. I like to buy my challenge maps at floor 100 or less (this makes it cheaper for the initial gold purchase then you will want to convert that map to Floor 401+). Immediately after killing each Enslaver, purchase a new map from the vendor, open and find the Enslaver as soon as possible. Do not be concerned or waste additional gold if the map you purchased is only normal or rare map → these maps are only bought to assist you to find the Enslaver. Using this method will enable you to kill between 120-360 enslavers per monster spawn boost.
With Accomplished Ascension, the new feats will be reduced by 25%. This means now that in order to spawn a legend Enslaver, you only need to kill 38 Epic Enslaver. This also reduces Legend Enslaver requirement from 10 to 8 in order to Spawn a Mythic Enslaver. With one Monster Boost and Accomplished Ascension, you now have the ability to obtain an Eternal pet during each boost if you are fast enough to each Enslaver during the 1hour boost.
Good Luck to all!!!