While it requires a lot of patience, a viable strategy is to restart until a Mini-Boss Room with Lust is encountered and that it drops The Virus. It will dramatically increase the amount of contact damage inflicted when throwing The Forgotten, making it much easier to attack quick or regenerative enemies. As a weaker alternative, obtaining Mom's Heels from a Boss Room will work as well.
While it does require some luck, visiting shops in possibility of Birthright and The Battery/Car Battery can grant invincibility in rooms while leading the bomb to enemies.
It's recommended to visit as many Curse Rooms as possible. Tainted Forgotten can enter and exit them without taking any damage, and they can provide precious soul heart health and powerful items such as Gimpy and Red Key.
Hence finding or buying Voodoo Head is a good help in this challenge.
It's also beneficial to bomb any Blue or Purple Fire Places the player comes across to gain as much soul heart health as possible.
The Forgotten will move slightly every time it explodes, unless the character has an item that grants flight. Using XII - The Hanged Man could prove useful for keeping The Forgotten in one spot for a room.
Picking up Gnawed Leaf is an instant win, as just holding Tainted Forgotten will provide permanent invincibility and free reign over where explosions occur.
Items that provide invincibility (such as Book of Shadows) or invulnerability to explosions (such as Pyromaniac and Host Hat) are very powerful in this challenge, especially when combined with orbitals such as Sacrificial Dagger. Not only do they nullify self damage, they allow Tainted Soul to safely carry Tainted Forgotten as it is exploding, greatly increasing the player's control over where explosions occur. Take caution if there isn't full invincibility, though, since Tainted Forgotten's explosions can still push Tainted Soul while being carried, which could push them into enemies that survive the explosion.
Room clearing items such as The Necronomicon and Flush! can be useful for skipping rooms that would otherwise be difficult with Tainted Forgotten's mechanics, such as rooms with lots of fast enemies. In addition, The Negative will trigger every time Tainted Soul takes damage, providing a good room clearing effect for the later stages of the challenge, though this should not be relied on too much due to the health cost.
The timer for The Forgotten's explosion resets every time a consumable is picked up or an active item is used. This can be used to avoid taking damage in certain situations. Items such as Converter, Sharp Key, Mom's Bracelet, Friendly Ball, and Bob's Rotten Head can be used to infinitely reset the explosion timer.
Since some bomb modifiers affect The Forgotten's explosions, playing the Bomb Bum can be quite powerful. Getting Blood Bombs, Brimstone Bombs, Mr. Mega, or Sad Bombs can be quite helpful as it will greatly boost the damage inflicted by The Forgotten's explosions. Glitter Bombs will be triggered with The Forgotten's explosions, allowing to generate infinite pickups. Bomber Boy, though, while boosting the damage, will also make dodging the explosions more difficult.
It is better to avoid Butt Bombs. This item can help a lot if fighting small enemies, but if you encounter the Brownie boss, unless you can one-shot him, you will heal him with butt bombs instead. This can cause a soft lock.
It may be good to skip the Devil Room on the second floor to ensure an Angel Room spawns on future floors due to Tainted Forgotten being a character that can't get heart containers, making devil deals inconvenient. This will also maximize the chances of finding Monstrance, an extremely powerful item for this challenge. On the other hand, the Devil Room can occasionally provide black hearts as well as Empty Vessel, which is also very powerful in this challenge due to its invincibility.
It is also recommended to avoid items that revive the player as a different character (such as Judas' Shadow), as upon revival the player will die immediately.
How to Jump can be used to stall the explosions of the forgotten, as the forgotten will not move and will not explode during the jump animation. Gaining flight is not advised, as it will prevent the use of How to Jump, despite regularly being usable by characters with flight.
Using Notched Axe will allow The Forgotten to do a melee attack. This also works as it's thrown, functioning similarly to Tainted Forgotten's regular melee attack, but without the charge attack. It also allows you to delay the explosion, as each time you use it, the explosion timer will reset.
Incubus will give the familiar to The Forgotten, granting you another way to deal damage more easily.
Twisted Pair will allow The Forgotten to use an attack similar to the bone swing.
Urn of Souls stalls the explosion indefinitely by spamming the use button to activate and deactivate. Should Tainted Forgotten also find Book of Virtues, then he can generate infinite flames, thus removing the reliance on explosions.
Super Magnet will pull enemies towards The Forgotten (and not The Soul), making them more likely to be hit with his explosions.
Mom's Bracelet allows the player to delay the explosion indefinitely, as The Forgotten will hold its arms up and reset its fuse.
Because Tainted Forgotten grants infinite explosion, it is recommended to destroy a maximum of obstacles to find rewards that might help. It's also a guarantee to find all Secret Rooms among other things.