Maybe a group of rogue demigods who have been corrupted by dark magic. They believe that by keeping the Doors of Death open, they can gain immortality or unlimited power. Percy would then have to face his own kind in order to close the Doors.
Another option is a primordial being that was awakened when the Doors of Death started to malfunction. This being is only interested in spreading death and decay across the world and sees the open Doors as a means to an end. Percy would have a huge challenge in front of him as primordial beings are extremely powerful.
It could be an ancient and powerful Titan who escaped from Tartarus when the Doors of Death started to malfunction. This Titan wants to keep the doors open to bring back all the old enemies of the gods and take over the world again.
Well, it could involve Percy facing numerous challenges in the underworld. Maybe he has to battle new and powerful monsters that guard the Doors of Death. He might also get some unexpected help from his friends, like Annabeth using her wisdom to figure out the secrets of closing the doors. And there could be a final showdown with some major villain who doesn't want the doors to be closed.
One idea could be Percy having to face his inner demons while closing the Doors of Death. Maybe past failures or losses resurface, adding an emotional depth to the task.
It could be a new, powerful and malevolent god. This god might be jealous of Percy's status as a hero and the favor he has from some of the Olympian gods. So, the new god devises a plan that makes Percy's life so miserable that he asks for death.
It could be the warden of the prison. The warden might be a cruel and power - hungry person who wants to keep Percy imprisoned for his own reasons, like getting some sort of reward or power from those who put Percy there.
A powerful dark sorcerer could be the main antagonist. He might be seeking to use Percy's skills for his own evil purposes, and when Percy refuses, he becomes the target. The sorcerer would have a vast array of dark magic at his disposal, making him a formidable foe.
It could be Orochimaru. Even though he's had his moments of redemption, he might relapse into his old ways. He could see Naruto's 'death' as an opportunity to carry out some evil plan that Naruto would have stopped. Maybe he wants to use Naruto's death to create chaos and then take advantage of the power vacuum in the ninja world.
Another possibility is that Death is being controlled or influenced by a greater cosmic entity. In this case, that entity could be the main antagonist. It uses Death as a tool to test or destroy the Avengers. The Avengers would then have to not only deal with Death but also find a way to face this more powerful and mysterious entity behind Death's actions.
It could be an evil shinobi who has somehow managed to control or manipulate the God of Death's powers for his own malicious purposes. This shinobi might use the power to create chaos in the ninja world, like raising the dead and making them fight against the living.
It could be a powerful rogue ninja who wants to use Naruto's new - found 'harbinger of death' status for his own evil purposes. Maybe he believes that Naruto can lead him to powerful and dark artifacts that are only revealed during times of death and destruction.