Now before I go into this, I'm a big fan of the Danganronpa series as a whole, so this review might be moderately biased. However, I'm going to try to keep it as seperate from my interest in the series as possible.
Please note that the series is VERY CLOSELY tied to the rest. Most of what's going on will be lost to you without knowledge of virtually every other released part- that being, Danganronpa 1+2, Ultra Despair Girls, Danganronpa/Zero, and even Danganronpa 3 Future Arc.
The story itself is about the characters of Danganronpa 2 and their time at Hope's Peak Academy, where they were all members of the 78th class. Meanwhile, Chisa Yukizome (the teacher of most of the characters), Kyosuke Munakata, and Juzo Sakukura are working on uncovering a conspiracy within the school, including the Kamukura Project.
It shows the gradual decline of the students and environment at Hope's Peak, an anime that starts out very cheerful and amusing and, as of the eighth episode, has made leaps towards despair.
While anyone who has played Danganronpa 2 to the end will know the fate of all the characters, Despair Arc has so far been important to worldbuilding, such as detailing Hope's Peak Academy's Biggest, Most Awful Event, Hajime Hinata's relationship with the main course, who the characters were before Danganronpa 2, what the Kamukura project entailed, the world's fall into despair, and will likely contain much more important information later on.
The characters are (in my opinion) interesting and likable, though most of the secondary characters do not get much screentime, and likely won't until they become involved with the main villain. The only exception to this I can think of are Chiaki Nanami, a dueteragonist in Danganronpa 2. The game's second dueteragonist, Nagito Komaeda, gets put on a bus and becomes irrelevant to the story for several episodes.
However, the build upon Chisa Yukizome, Kyosuke Munakata, and Juzo Sakukura, as well as other secondary characters in Future Arc (such as Seiko Kimura, Ruruka Andou, and Koichi Kizakura) makes both series much more interesting. The relationships between the characters becomes much more interesting, and if you are interested in Future Arc, keep in mind that you will only get half the experience without Despair Arc.
The sound is alright, with both the OP and ED being beautiful (the ED sung by Nagito Komaeda's voice actor), but most of the music in the show itself being... mediocre. Much of the soundtrack was reused from the original games, and while I don't have a problem with that, so little of the original games' soundtrack makes sense in the setting, thus leading to many instances of inappropriate silence. The sound effects are good, but also used extremely rarely, and mostly when a character uses a weapon.
I don't have much to say on the animation. I've seen better, and I've seen much, much worse. Ironically enough, the character Ryouta Mitarai is the best animator in the world, and is apparently making an extremely complex and well done anime by himself. Of the little they (understandably) show, he's shown using extremely complicated and difficult shots. None of these are used in the show itself. Some of the animation effects are interesting, such as those used in Episode 8, where the color scheme of the room changes dramatically into pastels very similar to those used in the OP before a traumatic experience.
I must say I think the page is inaccurate; while there's not a single main protagonist, Chiaki Nanami is the most likely candidate. Also, it's listed for "mild violence", but the later episodes have some explicit gore (including a drawn-out suicide scene which made my stomach flip).