Stories are all about the people in them (just like real life) and so of course, the most important scenes of any story are the ones where the characters experience intense emotions. It's important to portray them accurately, and strike a balance that neither downplays the magnitude of their emotions nor comes off as melodramatic. This is, unfortunately, really hard and I'm by no means a master of it myself. But I've learned a few principles from a lot of examples, both good and bad, that I want to share here.
It's almost always best to communicate the character's feelings through their thoughts that surround the emotion rather than directly using the word for the emotion. Example: instead of writing (assuming 1st person present) "I'm really mad at her", write, "What the hell! How could she do this and think it's okay?" Concrete thoughts like this make it far easier for a reader to imagine the character's feelings than just stating how the character feels. (This is an application of "show, don't tell".)
A related technique - these can and often should be combined - is to use the bodily reactions caused by many emotions. Mentioning how a character presses their eyes shut to begin crying or gets a pit in their stomach when they're afraid greatly helps the audience to imagine the character's suffering.
Another important element in applicable media is the use of music. Of course, a lot of this responsibility falls on the musician and not the writer, but there's still some decisions the writer can make.
- A lesson I learned from Doki Doki Literature Club: stop the music when the situation takes a sudden grave turn. Reading Yuri's second poem in Act 2 was terrifying, and this was why.
I think the reason this is so important is that it mirrors how we react. Most if not all of us, if something like that happened while we were speaking, would trail off our voices and give a moment of silence.
- Using dramatic or ominous music is really dangerous and needs to be done carefully, because it's one of the easiest ways to fall into melodrama. Dark Souls boss fights being the pinnacle example of course. Listen to this track and you'll see what I mean: music that just screams at the player "It's a big monster! Be scared!" is not scary or dramatic. It's melodramatic. Especially since in practice the only thing the player is afraid of is being sent back to the bonfire and having to run a mile back to the arena before they're allowed to face the boss again. For this to work, the audience has to already be invested in the characters and they have to take the danger seriously even before you added the music. Also, doing this in a video game is extra questionable because the player knows there aren't any real consequences - even for the in-universe characters - if they die. I'm not saying it's impossible, but I can't think of a time I've seen this done and not thought "Ugh, would you just turn off the damn music so I can focus on the fight, your bullshit gameplay mechanics facilitate more frustration than fear". Heroic music is almost always a better fit for games.
One pitfall I want to mention briefly is that having your POV shout their friend's name in all caps upon seeing them die is not realistic or relatable. It's not how a real person would react - none that I know at least - and it shows no thought, nothing that helps us feel with them. It's also incredibly cliched.
Now lemme talk about some examples of scenes in other people's work that worked and some that didn't.
Doki Doki Literature Club is a masterpiece in this regard. For an example, I'll go through MC's reaction to (major spoiler!) Sayori's death.
Next he has thoughts to the effect of "Is this a nightmare? It... has to be". The denial phase. It's human nature to look for any way to deny reality when you see something you really don't want to be true, even if only for a few seconds. The writer drags this out a bit, with the next lines being "This isn't real", "There's no way this can be real", "Sayori wouldn't do this", etc. This seems to bolster the effect; we don't want to breeze through these thoughts too quickly. A real person would probably spend several seconds at this phase, so the writer does too, even though it only takes one or two lines to make the point.
Next, as MC accepts it as reality, the writer mentions in his thoughts, "I suppress the urge to vomit". This line is a great example of using bodily reactions.
MC's thoughts continue into the main phase of grief and guilt, but he doesn't just think "I feel sad" and expect the player to sympathize. He goes through "I could have prevented this if I just did (xyz)!", "Nothing in my life is worth more than hers... but I still couldn't do what she needed from me", and "I'll carry this guilt with me until I die". These are concrete thoughts that do a very good job of making you shadow MC's pain.
Of course, a huge part of the magic of this scene was also the music it plays. That song captures MC's state of mind perfectly, and it's beautiful. The song is physically painful to listen to.
For a bad example, I could always criticize Star Wars. I know I've already talked about this but the total lack of any acknowledgement of fear really hurts the action scenes. How can you take these characters for real people when they don't show the slightest bit of fear getting shot at by a trained army and being trapped on the Death Star with no foreseeable way out? In real life, mortal danger is scary. Most people, if not fleeing or trying to surrender, would either be screaming or swearing their heads off in a situation like that.