Another possibility is that there is no real 'antagonist' in the traditional sense. Instead, it could be the circumstances that act as the 'antagonist'. For example, the differences in their worlds, their duties, and the fact that they come from such different backgrounds could be what causes Erza to break Naruto's heart.
Perhaps it could be a jealous character. Maybe there's a character in Naruto's world who is jealous of his relationship with Erza. This character could spread lies about Naruto to Erza, which would then lead to her breaking his heart.
Well, perhaps Erza might reject Naruto's feelings in a cruel way. Maybe she tells him she loves someone else, like Jellal. This would break Naruto's heart as he is used to being persistent in love, like his feelings for Sakura in the original series.
It could be Orochimaru. He might use Naruto's actions of breaking something related to Tsunade (like a seal she was relying on) to his advantage. Orochimaru could manipulate the situation to make Tsunade look weak or to cause chaos in the village.
Maybe it's a jealous rival of Naruto who wants Hinata for himself. He manipulates situations in such a way that Hinata ends up hurting Naruto. For example, he could stage events to make Hinata think Naruto has betrayed her trust.
Ino could be seen as the antagonist in this fanfiction. Since she's the one breaking Naruto's heart, she's causing the main conflict. Her actions are directly opposed to Naruto's happiness, which is a typical trait of an antagonist.
Another possible antagonist could be the Ministry of Magic. If they suspect Harry of something and force Tonks to spy on him or cut ties with him, it would break Harry's heart. The Ministry's strict rules and paranoia could be the driving force behind Tonks' actions that lead to Harry's heartbreak.
Well, in this kind of fanfiction, Dumbledore himself would be the main antagonist since the title implies that he is the one 'breaking' Harry. He would be acting against Harry's well - being and goals.
It could be Kabuto. He is always on the lookout for powerful items to enhance his own abilities or to use for Orochimaru's plans. The Heart Stone, with its mysterious powers, would be a great target for him. He might try to steal it from Naruto and use it to create chaos in the ninja world.
It could be a dark wizard who has a vendetta against Erza and sees her son as a way to get revenge. This antagonist might try to corrupt the OC son or use him as a pawn in his evil plans.
She could be a kunoichi from a small, unknown village who comes to Konoha on a mission. Naruto, being the friendly and trusting person he is, befriends her. But she has a hidden agenda and uses Naruto's feelings for her own ends, breaking his heart in the process.
It could be one of the powerful Edolas officials who oppose Erza's presence or her mission.