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Tear Jerker: Super Dangan Ronpa 2
The climax of the first trial, made worse because the culprit had one of the least selfish motivation of any killer in the series: not only did Teruteru attempt to stop Nagito and end up killing Togami by mistake, the reason he wanted to leave the island was to return to his ill mother. Especially upsetting because most had regarded the culprit as a one-note Joke Character until that moment, the revelation was enough to move several characters in-game to tears.
I'm sorry... everyone...
I didn't want to sacrifice anyone. I just... had to do something...
And yet... I ended up killing Togami instead of Komaeda...
Oh. I see.
It's me... I'm the one who went crazy.
There's also the part in the flashback when he tries to convince himself that his mother will be fine while he's away. He chuckles and says that he knows his mother "won't lose to some illness," but then repeats it more weakly, making it clear that he's not convinced at all.
On a related note, Nanami points out that it's most likely that the reason Togami died instead of Nagito was that, thanks to his night vision goggles, he saw Teruteru moving under the floor and moved to shield Nagito from the skewer...because he promised everyone that no one would die under his supervision.
The second execution: Peko Pekoyama. Just before it begins, Kuzuryuu breaks down into tears and begins screaming that he never wanted Peko to be his tool - he just wanted her by his side. Monobear takes control of Peko's body and forces her to fight an army of robots while Kuzuryuu tries to get to her, and she ends up slashing his face. Horrified, she cradles his body...and then the robots overwhelm her. Later, the characters discuss how lucky it was for Kuzuryuu to have gotten away in one piece, and they realize that Peko protected him as much as she was able to before she died.
Before the third execution, Komaeda expresses honest anger with the murderer for killing purely out of Despair rather than to inspire Hope. Mikan responds he's got it wrong: she killed out of love. When Komaeda's shocked by this, she talks about how someone accepted her for who she was, with all her flaws... and adds that she feels sorry for Komaeda, who's never felt that kind of love. It gets worse when you realize that the person she's talking about is Junko, who more-or-less brainwashed Mikan into joining SHSL Despair and who probably never gave a crap about her at all.
The fourth trial and execution: Gundam Tanaka and Nidai Nekomaru. When the entire group was left with nothing to do but starve to death, these two decided to try to "kill each other" just in order to have a murder committed, and therefore get food to all the rest of the group who needed it. By the end of the trial, every character seems to understand that for Gundam and Nidai, this was actually their sacrifice to save the rest of the group from a prolonged and painful death.
Not to mention Gundam saves his hamsters by placing them out of the way before facing his own death.
His hamsters cry for him.
And then his dead pets carry him to heaven...I'm not crying, I'm not crying...
Sonia's reaction to the whole thing is saddening as well. Gundam is arguably the student she is the closest to and when she finds out he is the murderer she is completely shocked. Even so, she cries and pleads with Monobear to not execute Gundam because she understands that he did it all for their sake. Gundam's last words are also what motivate Sonia to continue surviving and to not give up on the investigation in Chapter 5.
Akane is usually the toughest and most aloof of the students, and the only time we've seen her cry before was when she was infected with the Despair disease. So seeing her genuinely sobbing while cradling Mecha!Nidai's head was especially heartbreaking. It gets worse when you learn about her life growing up. Akane never bothered to make close friends, or even learn any names, because there was always a chance they were going to die the next day. But at this point she had become extremely close to Nidai. She allowed herself to become close to another person, only to lose them. And it was soon after she almost lost him the first time too.
In Chapter 5, you can see Kuzuryuu stopping at the memorial. He finds a picture of himself with Pekoyama, who's been dead since the end of the second trial, and realizes that this was the only one of them together as friends and classmates. Hinata wonders if Kuzuryuu has been crying, and decides to leave him alone.
The fifth trial and execution: The kids determined that Komaeda committed suicide, and we figured that was it—vote him as the culprit, no one else has to die. Except that he actually set up an awful plot which created an accidental culprit, so even though the entire plan was set up and carried out by Komaeda, the actual cause of death is laid upon none other than sweet little Nanami. This was all part of Komaeda's plot to kill the rest of them so that only the traitor would live, but Nanami wouldn't allow that—as soon as she figured out the truth, she decided to sacrifice herself to save her friends, and that was truly one of the most unfair and heartbreaking moments of the entire game.
The execution itself punches the player in the gut. In the previous chapter, it was pointed out that every murder in this game has been similar to a murder in the first game. The fifth execution in DR1 had Naegi escape and survive until the next game. Naturally, when Nanami spots an exit door in her execution chamber and makes a run for it with Monomi, the player expects the same scene to play out. Nope! Nanami and Monomi get trapped in a giant game of Tetris and just sit there miserably until Monobear drops blocks on them and kills them. It doesn't help that he stretches out the moments before finally killing Nanami forever.
Another particuarily heartbreaking moment is everyone's attempt to deny the fact that Nanami is the culprit, especially Sonia. There is an instance where you have to play the counterargument game against Sonia, and instead of playing the usual high speed and volume theme that goes with the game, what instead plays is a quieter song appropriately named "All All Apologies".. It shows how much pain Hinata is going through... He really doesn't want to see one of his greatest friends dead, but at the same time, if he wants everyone else to live, he has no choice.
On a related note Monomi's PTA and her dialogue leading up to it. she's such a Bad Liar, everything she says about Nanami is the exact reverse of their true relationship. She has a friend and she loves Nanami.
What really hammers it in is Hinata not doing his usual dramatic voice clips when breaking arguements and selecting the culprit. He's either completley silent or has new ones that reflect just how much he doesn't want to go through with this.
The game also has a departure for all the other trials. When the time comes to vote for the culprit, the game makes you vote for Nanami yourself.
When you find out that Komaeda didn't just have a moment of trollish insanity when his aim was to kill everyone but the mole: He learnt that everybody, including himself, were the remaining members of SHSL despair and that the mole was from a foundation trying to purify the world from despair. Out of the horror of this truth, he aimed to kill himself and the rest of the people who once bought despair into the world, leaving the one person (the mole, who did not cause any despair) alive. Komaeda's mental condition made him take this news so badly, that he wanted everybody who caused such despair to be gone from the world. He had good intentions, poor guy.
In Chapter Six.
One of the reasons Hinata's so wary about the Forced Shutdown is because it'll get rid of everything in the game world - and since Nanami was an AI who never exist outside of the game, they'll forget her entirely.
Also during the final trial, the main reason why Kuzuryuu is reluctant to invoke the forced shutdown isn't because he doesn't want to go back to being Super High School Level Despair (although he's also against that)- it's because he wants to see Peko again.
The part of the trial where Junko throws Hinata into an Imagine Spot where the game has reset and everyone is alive and well. They are all happy and acting like regular high school students, with no signs of despair. But it's all a sick lie that can't come true without severe consequences in the real world.
Everything about Izuru Kamukura, once you get past the Nightmare Fuel. He started out as an average reserve student who just wanted to gain a talent and escape his second-class status, and ended as a mass murderer, bitter and bored with existence. Chapter 0 (the short scene at the end of Chapter 5) shows just how empty and apathetic he's become, with no trace of the cynical but good-hearted Hinata left.
There's also Hinata's breakdown upon being confronted with this revelation, particularly in the English version. Johnny Yong Bosch did a really good job.
Both himself and the other students have to come to terms with the fact that, since Hinata's personality was created for the game world from what remained of Izuru's memories, initiating the forced shutdown essentially means killing him. The other students may have been brainwashed by despair, but it would still be possible for them to return to who they used to be. Hinata and Chiaki, however, would be gone forever... and they wouldn't even remember them. Fortunately the epilogue shows Hinata is okay after all.
Pretty much every character's backstory. Most notably:
Peko Pekoyama: abandoned as a baby and raised to think of herself as only a tool to serve Kuzuryuu.
Mikan Tsumiki: bullied so mercilessly that she thinks degrading herself is the only way to gain attention. It's implied that she was in love with Junko, who's the one behind the killing.
Kazuichi Souda: bullied at school to the point that he tried to completely reinvent himself into a tough guy jerk, because that's what his bullies were like and he associates that behaviour with strength. He was also implied to be abused by his father.
Akane Owari: grew up in poverty and has worked in jobs were she was sexually harassed, all to gain money for her several siblings. In chapter 4, she says that the cheap room in the funhouse is a palace compared to her home.
Nagito Komaeda: his life has been a constant cycle of bad luck, good luck which has included losing his parents in a plane crash, then gaining a massive inheritance, then him being kidnapped, then winning the lottery. Lately, he's also been diagnosed as terminally ill. This cycle has exhausted him so much that in his Dangan Island ending, it's revealed that he wanted to die on the island.