There's a chance that Percy meets the personification of Tartarus itself. It could be a shadowy, all - powerful being that tries to break Percy's spirit. Percy, being the brave hero he is, would have to resist and find a way to either outwit or overpower this entity in order to continue his journey in Tartarus.
As for enemies, Percy could encounter the Titans who were once banished there. They might see Percy as an intruder and a threat, and try to eliminate him. Also, the monstrous creatures that lurk in Tartarus, like the Empousai or the Chimera, could be his foes.
Perhaps Percy has to go to Tartarus alone because he believes it's the only way to save his friends. In Tartarus, he might encounter old foes who are now even more powerful. He has to rely on his wits and his skills with his sword, Riptide. He could also make unexpected alliances with some of the creatures there in order to survive and achieve his goal.
It could be Tartarus itself personified. As Percy is alone in this terrifying place, Tartarus could take on a form and directly oppose him. It would use all the horrors and challenges of the place to try and break Percy.
In this fanfiction, Percy going through Tartarus alone could involve him exploring the darkest parts of the underworld. He could discover secrets about the origin of the monsters there. Maybe he stumbles upon an ancient power that he has to either resist or use to his advantage. Along the way, he might have visions of his loved ones which both give him strength and also make him homesick.
Bob the Titan could potentially be an ally. Since he has some knowledge of Tartarus and has shown kindness before, he might come to Percy's aid again. He could help Percy navigate the dangerous areas and avoid some of the more powerful threats in Tartarus.
Well, one possibility could be Percy facing his inner demons. In Tartarus alone, he might have to deal with the memories of his past failures and the fear that comes with being in such a desolate place. He could encounter strange and terrifying creatures that test his combat skills and his will to survive.
Perhaps Percy will meet a group of environmentalists. Given San Francisco's reputation for being environmentally conscious, they could be fighting against some sort of sea - related pollution that Percy gets involved in. He might use his powers and knowledge to assist them, and in the process, make some good friends.
There could be a school janitor who is actually an old demigod who retired from the hero business. He could give Percy some valuable advice based on his own experiences. And of course, Percy will surely meet Annabeth's classmates, some of whom could be friendly and some not so much, depending on how they react to the new boy in school.
He could meet some Aboriginal heroes or spirits. They might have their own powers and knowledge that Percy can learn from.
He might face numerous terrifying monsters. Tartarus is full of dangerous creatures, and without his friends, Percy would have to rely solely on his own skills and the power of his demigod abilities to fight them off.