This is based on opinion. Please don't list it on a work's trope example list.
Tearjerker / Hajime no Ippo
Both title matches for Aoki and Kimura could be considered this, much more the latter since the end result prompted Kimura to retire.
Kimura's title match was already bittersweet as it is. Kimura loses? He retires. Mashiba loses? Hints of more struggles for both him and Kumi await.
A good chunk of the fighters' backstories.
Ippo: Father died during a fishing expedition, had to help his mom run the fishing boat as a child.
Sendo: Mother died during childbirth, father sacrificing himself while doing his job as a fireman.
Miyata: Witnessed his father get utterly destroyed by Randy Boy Sr., watching him turn to alcohol and seeing his mom leave the family, while still wanting to follow in his dad's footsteps as a counter expert.
Mashiba: Parents died in car crash, had to raise himself and Kumi while still only a teenager.
Date: Lost against Ricardo Martinez, then learning that his pregnant wife got into an accident which killed their unborn child.
Sawamura: Father died, mother got into an abusive relationship, which abruptly ended with Sawamura stabbing him. He was abandoned shortly thereafter.
Volg: No news about his father, his mother winds up being really sick so he takes up pro boxing to help her get better. Made even worse when we find out he fails.
Gedo: Had to steal money in order to survive, eventually being shot in the shoulder, and then losing to Randy Boy Jr. during his championship match.
Nekota: Fought with Kamogawa to the point where he became Punch Drunk, causing a Game-Breaking Injury against Anderson when he fought.
Kamogawa: Fought with Nekota to the point where Nekota became Punch Drunk, injured both of his fists in order to practice the Tekken, then shattering them both in his match with Anderson, forcing him to retire in spite of his win.
Ryuhei Sawamura: Retired as the Japanese Jr. Lightweight Champion.
More specifically, it's been mentioned at various times before, during and after the match, that Sawamura was earnestly trying to win the belt. Despite all that cheating and injuries sustained, he got what he wanted... only to get into a motorcycle accident that leaves him unable to fight in the ring anymore.
Another heart wrenching moment is After Sendo has defeated Volg for the championship, Volg's contract with his gym had been severed, and could have been severed any time he lost too many matches. Volg's farewell to Ippo at the airport, knowing that they might never be able to meet again, is incredibly heart breaking. Specially when Ippo can hold back the tears when in front of Volg... but he breaks down crying once he's gone.
Former bully-turned-friend Umezawa is out of work and comes to Ippo's fishing business as a hired hand, so Ippo can keep up with his training and his mother won't overwork herself again; he also plans to use the experience to write a manga about Ippo's rise in boxing. After just the first day he feels so horribly overworked (and his seasickness doesn't help matters, either). As Umezawa turns the corner to return home after work, Ippo guesses that the difficulty of working in the business was too much, and that he won't come back the next day. In fact, Umezawa stopped around the corner, breaking into tears because he feels so useless, unable to help Ippo. The next day, however, Umezawa is waiting for him, ready to start the day with a grin and a determined attitude.
Watching Takamura of all people bawl his eyes out when he finds out the bear he spared (because she had cubs) got shot and turned into his stew is pretty hard to watch. Mostly because Takamura can apparently be quite motivational when he's feeling strongly about something.
In Champion Road, Takamura, Aoki and Kimura badger Ippo into confessing his love for Kumi; after the date, when they think they're alone, she encourages him to say it- but because this is Ippo we're talking about, he loses his nerve and instead tells her he has no right to tell her who to cheer for. While this is meant to show his lack of self-confidence, she takes it as him not caring whether or not she cheers for him, and wordlessly leaves him. Ippo's face is one of shock, and worse, Takamura, Aoki and Kimura have been eavesdropping- not a single one of them feels good about what just happened, prompting Takamura to suggest they just head home. The next day Ippo is training hard, and Takamura points out that after losing Kumi defending his title is all he has left to look forward to. Inwardly, he genuinely feels bad about what happened- it was not what he wanted for Ippo. The two get back together in the end, but it's still a sore part of the story.
Eiji Date's rematch against Ricardo Martinez. An accidentally made Game-Breaking Injury is what lead Date to not only lose against Ricardo but also retire from boxing permanently.
Newer member Itagaki Manabu has his first debut match against underdog, Makino Fumito- a dismal boxer who at the time had two matches, both losses. Itagaki was expected to win the 4-round, 2-down match, being a prodigy boxer- the match ends in his loss when Makino commits two fouls, the first being a headbutt; the second being an elbow strike. The referee somehow sees neither of these. When Ippo visits him in the locker room, Itagaki is torn up over it, stating that he stepped into the ring expecting to box; but that it doesn't feel like he was in a boxing match in the slightest. Worse, Ippo tries to tell him that it's not a foul if the referee doesn't call it, and that Itagaki's appeal during the match caused him to lose focus, and that the fault lies in him for not maintaining focus. As one might expect, he does not take this well, running from the stadium distraught and disillusioned.
How about Saeki's match against Itagaki? Seeing him lose like that is heartbreaking, because he was fighting for Karasawa, who retired but was unhappy with his life. This is likely something that happens among boxers in real life, which is harsh.
Aoki and Kimura's second shot at the Class A tournament ends this way. Kimura loses mostly due to just not having the drive to fight harder, while Aoki gets pummeled and hospitalized by Iga (who was instructed to hold back to prolong the suffering). Even worse, Yagi says he would recommend that the two retire, and next chapter shows that they were seriously considering it. They ultimately decide to keep boxing, but it was a bleak point in the story, nonetheless.
It gets worse after that, a few chapters later, Kumi up shows the day after Ippo's loss to have a talk with him, it takes a second to sink in but it is made clear and blatant that she is trying to convince Ippo to quit boxing. Ippo reasserts his ambition to keep on fighting, feeling like he let his gym and coach down, again, but after that he...gives Kumi a promise, all with a determined yet solemn look on his face:
Ippo:*after looking at Kumi for a moment*...I know. I don't want my mom to worry too much, so...this is the last time. This will be my final challenge. Next time I lose, I'll retire with no regrets. *Starts walking away from her* I'll never fight in the ring again.
And of course we have Kumi herself here. She knows how much Ippo loves boxing, how much it means to him, the fact that she probably wouldn't have even met him were it not for boxing. But after his second defeat she probably remembers how hard his first loss hit him, and doesn't want him to suffer anymore. And all of that starts when Kumi asks Ippo a very simple question that throws him completely off balance:
Ippo's shaky handwriting. It's one of the sure signs that Ippo might be suffering from brain damage, but neither he nor the audience knows for sure...
In chapter 1197, Coach Kamogawa's realization that Ippo really is suffering from CTE/punch drunk disorder. The look on his face is heartbreaking.
The final episode credits of Rising dedicate the whole season to Kenji Utsumi and Ichirō Nagai, who are the respective voice actors for Kamogawa and Nekota. Utsumi passed away in June 2013, therefore having to cast another VA for Kamogawa, and Nagai in January 2014.