Buckle up yall, I'm going on a rant about how I think Junko got power over each Remnant of Despair (ignoring the canon brainwashing because I hate it, it makes no sense). Warnings for death mentions, different levels of manipulation, and trauma being used against people.
Y'all ready? Okay.
Imposter was a tiny bit difficult, but nothing Junko was unable to control. They probably felt empty and wanted a chance to exist without impersonating someone, so Junko likely just made a promise and used a little bit of sweet talk to trick them into believing that her plans would let them just exist and be able to do what they want. The despair of knowing that you basically don't exist would break them eventually.
Teruteru, simple leverage and threatening, probably blackmail too. Junko likely has ways to look into everyone's pasts and relationships, so she probably dangled the life and prosperity of his mother and the family diner over his head as a way to force him into things. It probably escalated at some point, and ended up just outright becoming what he wanted to do himself. If you put enough pressure on something, it will break eventually.
Mahiru took a little effort maybe, but Satō's death and the guilt of having a bit of involvement in Natsumi's death weighs down on her and thus Junko was able to make her believe it really was all her fault which in turn drove her into despair.
Peko was simple, all she had to do was get Fuyuhiko on their side and Peko would follow. Junko would've probably just killed Fuyuhiko too if he wasn't useful to her, so maybe Junko threatened his life which made Peko desperate to do anything to ensure his safety. Her entire existence revolved around his, and if something happened to her, she would be useless. The thought made her frantic and plung into despair due to that.
Ibuki wasn't difficult due to her IQ. Ibuki wasn't the brightest, but she was useful in some aspects. Junko probably went with either tricking her, or using popularity and relevance as leverage aswell, maybe even using other classmates again. Ibuki got a little anxious, and it spiraled over a long period of it into a state of despair at the constant worry.
Hiyoko took some time, but her own past was in play and used against her. Junko likely promised she'd be able to see the people she loved again and that the pressure from popularity would stop. Hiyoko likely fell apart when she realized she wasn't going to see her only loved ones again, and like the rest broke and fell into despair.
Mikan was one of the easier targets. Her issues with her past and her constant anxiety made it easy to get her to attach to Junko. Mikan was so used to being mistreated that just a slight bit of positive affection or even just a bit of praise got her to follow Junko around and cling to her, she's traumatized and unstable and was easy to control. Even the slightest bit of negativity from Junko after that would cause her to spiral towards despair and make her desperate for the rare positivity.
Nekomaru took effort, but once again it was likely the childhood. Since he was bullied for his name (at least if I recall correctly) she likely used that as a "Don't you want revenge?" tactic. Maybe she used his heart condition too, "you'll only live a certain amount of time, use it for what's really important." He reflected and realized he was doomed to die and his childhood was nothing but pain, so he tripped and smacked into the floor of despair.
Gundham was simple; his loved ones and his childhood made it easy. She could've easily used the Devas against him or even his mother, and probably made comments about his father and the people around him growing up. The Devas were dear to him, so she likely used an anger and desperation tactic and made him feel despair out of worry for them.
Nagito was both easy and difficult. He was so dead set on the fact that Hope was always triumphant, it took a bit more. She probably made him reflect a lot on his childhood, the treatment he faced daily, probably berated him then gave him rare praise, took time to slowly ease him away from his Hope mindset and into Despair. He was a process, but he eventually submerged to Despair when he finally gave up and thought, "What's the point in continuing on if my luck and presence will only torment everyone?"
Akane was yet another game of Childhood Trauma as a weapon. The childhood she faced was rough and she was still not stable from it, Junko probably exposed her to things that reminded her vaguely of her childhood that got progressively more dark as it went on. Junko used the fact that Akane would jump and snap into action as reflex, and she trained her like an animal to pounce at things. Akane slowly drowned in her thoughts of her life and it turned to a despair-ridden rage.
Kazuichi was merely another childhood and peers case. "You'll never be loved by anyone," she said, "You'll never be loved romantically, and probably never were in a platonic or even familial way." She would repeat. She'd break him slowly by using everyone else and probably claimed to be the only one who cared. Kazuichi is highly emotional, and he fell into despair rather easily since he -like most teenage boys- probably cared a lot about how people viewed him.
Fuyuhiko was easy. "You were raised to kill and hurt others mercilessly, do the one thing you're good at." She told him. Natsumi's death, the pressure of his life, whatever traumas he experienced as a kid. They all added up. He knew what he was capable of, and he probably subconsciously wanted to act on it. Put too many things onto one thing and it'll eventually topple over onto that one thing, he was crushed by the weights on his shoulders till it made him drop to one knee in the face of despair herself.
Sonia was quite literally "Aren't you tired of being nice? Don't you wanna just go apeshit?" Her life was dictated by her social standing. Taught from birth to be one way, ignore all interests and indulge in one goal. "You are not a person, you're a leader." Junko would remind her, then claim she was so much more than what she was taught. She grew sad, then angry, then cold and sadistic. Despair made her emotional and irrational, so she acted out of impulse and revenge.
We know Izuru joined Junko just because he was bored and wanted entertainment, but I don't believe it was that simple. He wanted entertainment, yes. He was bored, yes. But that couldn't be all, right? He's strong, mentally and physically, at least he was supposed to be. He was so tired of the calculating life he lived, tired of not knowing who he once was, and tired of how tired he was, and it probably gave him a subconscious sadness. He grieved himself without realizing it, and he was probably not mentally stable due to his existence. Junko took advantage of it. She knew he was bored out of his mind, so she promised him ways to feel something other than empty boredom. "In a world without them, you can do whatever you want. You can find out who you once were, you can watch people act out of Despair and Hope, and you can even watch Despair and Hope battle till only one remains." She'd convince, speaking innocently till she brought him into a sense of false security and then turned it all around and left him to his own devices when she started THH.
Of course, there's also Chisa. She was exposed to the first Mutual Killing Game, and it hurt her emotionally. That couldn't break her though, logically it made no sense for that and the Reserve Boy to be what broke her, and the literal lobotomy didn't make sense. Sure, exposure and warping of the mind works, but Chisa'e actions come from her heart. So I think it'd be more fitting if Junko had used Chisa's loved ones as leverage. Kyosuke, Juzo, class 77, they're all important to her and she loves them dearly in their own separate ways. So Junko probably used all of their wellbeing against her, and she acted out of desperation and panic, cracking and shattering into shards of Despair slowly when Junko would speak.
Then, Chiaki was the cake on top of it all for them. Her death would ruin the tiny hints of sanity they clung to subconsciously, and it'd send waves of Despair through them all at once.
Class 77-B was her perfect target, and Izuru and Ryota were what she needed to help that plan become reality. She used her charms and their weaknesses to her advantage, and they ended up worshipping her as a savior. She "woke them up" in a sense, that's what she told them at least. In the end, she had some victory, but we all know how that played out in the end. Moral of the story, don't be batshit like Junko and try to watch out for people like her!