Eve

Repentance 1.7.9 on PS5.

What you start with

The mechanics that actually govern this character.

2 red heart containers, damage multiplier 0.75, speed 1.23. The multiplier rises to 1.00 while she is at one full red heart or less.
Whore of Babylon and Dead Bird both trigger for Eve at one full red heart instead of the usual half heart. Whore of Babylon is +1.5 damage and +0.3 speed.
Razor Blade (439 coins donated to the Greed Donation Machine) lets her self-damage into her power state on demand, and Razor Blade damage counts as self-damage so it does not lower Devil room chance.
Heart drops have a 16.25% chance to be replaced by a soul heart for Eve, against 10% for everyone else.

Her real stat line is 1.00x damage plus +1.5 damage and +0.3 speed, and she only has it at one red heart or less. Anything above that is a nerfed Isaac.
On floors 1-2, spend red hearts deliberately: Curse Room doors, Blood Donation Machines and Devil Beggars all count as self-damage and none of them reduces your deal door chance.
The Whore of Babylon effect switches off when you leave a room holding more than one full red heart, so do not grab red hearts unless you intend to spend them immediately.
Soul and black hearts are how she survives at one red heart, so Book of Revelations, Satanic Bible, Mitre and Dark Bum outrank plain HP ups for her.
Curse Rooms are her best early room: the door hit puts her into her power state for free, and the room itself can hold soul hearts, black hearts, Dead Cat and other Guppy items.
With Razor Blade unlocked the calculus flips: take heart container ups freely, because you can always cut back down to one heart inside a room with enemies.

Strong on this character specifically, not just strong.

Birthright: Whore of Babylon is active regardless of health and Dead Bird is active without needing to take damage. Do not reroll or lose either starting item afterwards, or the effect stops.
Razor Blade: on-demand entry into her power state, its own damage boost, and no Devil room penalty.
Dead Cat, Guppy's Paw and Abaddon: items whose cost is red containers are pure upside on Eve, since the containers are what she wants gone.
Blood Oath: the start-of-floor stab drains all red health, which guarantees Whore of Babylon every floor and pays exponential damage for the hearts drained.
Empty Vessel: in Repentance she can drain red health while keeping soul hearts, so she can sit at zero red hearts with permanent flight and a recurring 10-second shield.
Athame or Maw of the Void: reliable black heart generation, which is health she can actually hold onto.
Dark Prince's Crown and other low-health triggers, which are permanently on for her.

Picks that are neutral or good elsewhere and bad here.

Placenta, Charm of the Vampire and the Tick trinket: they refill red hearts and switch her out of Whore of Babylon without asking.
Magneto and the Super Magnet trinket: they drag red hearts to you, which can push her above one heart and cancel the effect mid-room.
Child's Heart trinket: more red heart drops at the cost of bombs and keys, which is the opposite of what Eve wants.
Health ups before Razor Blade is unlocked: containers you cannot cheaply spend just keep her at the 0.75x multiplier.
The classic Razor Blade plus The Polaroid invincibility-spam damage stack is Afterbirth-only. It does not work in Repentance, so do not build around it.

Verified against 1.7.9 on console — anything patched, PC-only or Repentance+ only is called out rather than listed.

Curse Room doors, Sacrifice Room spikes, Blood Donation Machines, Devil Beggars, IV Bag, Sharp Plug and Razor Blade all count as self-damage: none reduce Devil room chance and none destroy the Perfection trinket.
Because she wants to be at one red heart anyway, Devil deals are functionally free. Convert containers into items on the way down instead of losing them to enemies.
Blood Oath triggers Whore of Babylon unconditionally at every floor start, and it does so even if she is holding only Rotten Hearts.
Empty Vessel's shield is 10 seconds out of every 40 in rooms with enemies, which pairs directly with running her at deliberately minimal health.

Her power state requires low health, so Chapter 4 onward is where she is punished hardest: every hit becomes one full heart, which is her entire buffer.
Her Devil-leaning economy makes Satan and The Lamb the natural mark pair. Chasing Mega Satan instead means refusing every Devil deal, which costs her most of her item income.
Dead Bird persisting between rooms at low HP of any heart type is a Repentance+ change. On 1.7.9 Dead Bird only lasts for the room in which you were hit, so do not plan around a persistent bird.

Open the tracker for the ordered run queue, or how to unlock characters if this one is still locked.