This is how I obtained the achievement. I recommend you read this entire guide before you attempt it:
1. Play as Cain, for the Rabbit's Foot. *Luck Boost Perk. Most of your gambling will be successful.
2. Obtain the IV Bag and "Portable Slot" Machine on the same floor, so you can keep alternating between them. *I managed this from an arcade room for the IV Bag, after the blood bank exploded. I either got the Portable Slot from a Treasure Room or Angel Room. You can also carry one of these items over from a previous floor and hope a future floor will drop the other.
3. Use the Portable Slot for heart drops. *You will get a bunch of pills, bombs, and keys, too. The pills are fantastic on Cain, as he will never have negative pills. (Only neutral or positive).
4. DO NOT PICK UP ETERNAL HEARTS UNTIL THERE ARE TWO HALVES ON THE GROUND.
*BEWARE TELEPILLS. IF YOU ENCOUNTER "ERROR," YOU WILL PROCEED TO THE NEXT FLOOR.
**The room will be littered with items, or you will be out of money. Pick everything up, besides eternal hearts, unless there are 2 halves, as mentioned. ***Eternal hearts have a 1/50 chance of replacing a heart drop.
5. With the IV Bag, rapidly press the space bar to get a bunch of money. Depending how fast you are pressing it, you can use the IV Bag 2 or 3 times for 1/2 heart. *This is a money bug you can exploit, and I recommend it. It takes a lot of luck and patience to even have the Port Slot and IV Bag at the same time, so you deserve it!
6. I recommend grinding this until you have max health. In normal mode, you can have up to 12 heart containers, plus 12 full soul hearts, for a maximum of 24 hearts. In hard mode, the maximum is increased. *I stayed in an arcade room for about 2 hours doing this method until I was satisfied. At this point, I also had almost maximum money, keys, and bombs. 3 of my 4 skills were over the maximum bar. I was quite giddy, I may add.
This method will give you the "Eternal Life" achievement, and will almost guarantee your success in the playthrough. Good luck!