Eternal ???

Taking dead cat will set you down to 1 blue heart. Using items that make you invincible (like the chariot card) can give you devil deals for free. Despite what the wiki says, Guppy's Hair Ball does count for guppy transformation with the eternal update. If you hold up on the top wall red flies will be unable to hit you (unless pushed by other enemies/more flies.)

It is very important to keep your health up as ??? because it cannot be refilled. Items which give soul hearts such as the Crystal Ball, Book of Revelations and the Nail are useful to keep him alive. Arcades are important because they can give you more soul hearts, spend all of your extra money on the fortune telling machines and if they break you can spend the rest on the skull game, and last resort slot machine.
Items that reveal the map such as the compass can be extremely useful to prevent damage in unneeded rooms. Since the Crystal Ball essentially combines the effects of the map, compass, and book of revelations, it is very strong for ???.
Aside from health, flying and orbitals such as the Guardian Angel will help keep you alive. You will also need damage to take down the bosses before inevitably getting hit. Guppy is incredibly powerful as it gives flying and a lot of unmissable damage. Ipecac and brimstone are also powerful, and if you rapidly tap the direction you want to attack with brimstone you can do up to 5 ticks of damage instead of 2. (Search brimsnapping for more info.)
Only take the best of devil deals unless you can get them for free using invincibility, do not go into curse rooms (unless high on health and close to guppy), and do not do challenge rooms unless necessary. Boss challenge rooms and eternal challenge rooms can be a good idea if you have enough damage as they will usually give you at least 1 heart.
TL;DR: Health, Map, Flying, Orbitals, Damage. I finally managed to do it with crystal ball and guppy.
Check here for more useful strategy for ??? including a list of useful and bad items: ???/Strategy[bindingofisaac.wikia.com].

Keep an eye out for Tinted Rocks[bindingofisaac.wikia.com] and Secret Rooms[bindingofisaac.wikia.com] and even Super Secret Rooms[bindingofisaac.wikia.com] if you have enough bombs. You can hold R to completely restart, you can use this if you get a horrible item on the first floor.