Each time Naegi figures out the culprit and how the crime occurred, right down to every last minute detail.
Especially when Naegi finally figures out, in chapter 6, who the mastermind behind this whole fiasco is. Made even better in that Naegi's chain of reasoning began because he noticed something as small as there being only 9 indicator lights in the morgue instead of 10!
A while after Chihiro is dead, we learn about hisother CMOA. Instead of (very understandably) freaking out at Monobear's Educational DVD and the threat of having him reveal Chihiro's gender/identification to his newfound companions... Chihiro softly and politely tells Monobear that no, he won't play his game, that he won't bend over to his wishes, and that he will tell the others he's a boy when he feels ready for it. Cute little Chihiro has discovered that yes, he DOES have what it takes to be strong, and this will lead to the creation of several AI's that will protect his friends even after he is gone.
Mondo and Chihiro symbolically lending their aid from beyond the grave. Mondo's spirit fuses with Kiyotaka, and Chihiro leaves behind Alter Ego, a program that can help connect with the outside world.
Mondo's reaction to his execution, being tied to a motorcycle and sent into a "death cage". Unlike Leon, he doesn't struggle or attempt to escape the motorcycle in any way, accepting his punishment for killing Chihiro.
Asahina slapping Togami across the face for being such a Jerkass.
After the fourth trial, everyone (even Togami and Fukawa, in their own way) stand up and tell Monokuma they're done playing his game, and that they'll be working together to take down him and the mastermind.
Sakura Oogami gets a post-mortem crowning moment of awesome when it's revealed what her "first shot" against Monobear was: Sakura broke the lock to an important door Monobear was guarding so Kyouko Kirigiri could break in and see what was inside.
The true ending of Chapter 5. Naegi's about to be crushed to death for a murder he didn't commit, when...surprise! Alter Ego turns out to have uploaded a virus to the school's network! The virus opens a trapdoor under Naegi's feet, robbing the piston of its intended victim, just in time, much to everyone else's shock!
Naegi mirroring Kirigiri's reaction to it is impressive, when you think about it. The player's first assumption would probably be that he'd freak out.
The best part of the whole scene? Monokuma's little Villainous Breakdown right after Alter Ego's rescue. After spending so much time looking down at the students, laughing at and blaming them for descending into despair, he's finally getting a taste of his own medicine. And you can just tell that it tastes bitter. So. Very. Bitter.
Bonus: Chihiro wanted to be strong. Alter Ego—essentially a digital copy of Chihiro's personality—has become strong enough to hold back a killing machine.
There are quite a few of these in Dangan Ronpa IF, including Mukuro Ikusaba being able to match fists with Sakura Oogami, Mukuro fending off hundreds of Monobear units, Oowada and Sakura saving Mukuro from said units (including Oowada riding the motorcycle used in his execution), and Mukuro's gambit to get through the Final Graduation Exam.
On a meta level, the game is getting a western release effectively because of a Let's Play - one from Something Awful, no less.
For the anime: The Reveal of the Mastermind's identity. Not being limited by sprites limitations is a good thing.
Also, Naegi going more than "You must not lose hope!" to instill hope to his friends, he frigging tailored A LOT of Rousing Speech to raise their spirits and it works!