Bucchigiri is a great show, with great premise, amazing jokes, really good character design and music that is out of this world. While the animation isn't excellent, it's really good for an anime that is heavily focused on fighting.
That, to me, sounds like a 10/10 show. However...and that is the problem, there is a however.
Bucchigiri tried to do a lot at once and seemingly ran out of time... Let's break it down a little more.

HUGE spoilers incoming.

Story:
(This is my rant of why the story is confusing, what plot holes it has and why it doomed the anime.)

Arajin meets two important people in his new school. Mahoro Jin (the sister of the head of Siguma Squad) and his childhood friend Matakara. Arajin only has two wishes - 1) to loose virginity (preferably to Mahoro) and 2) avoid fighting at all cost. However, not only does Matakara want to patch things up with him and continue training to become Honki people... Marito Jin takes liking in Arajin and wants him to join his squad & fight for fun.
We can't forget to mention the mysterious man (I think he is actually Arajin's teacher???) that goes to Nyan Nyaight Love to see a certain Jasmin-chan... (They have their own side story).
Of course that is not all. This show also has a genie! His name is Senya and he can merge with Arajin for ultimate power.
But Senya too has a past that comes back to haunt him...

Confusing? Hard to follow? All over the place? Well, exactly. This story has many plotlines they are following and you loose track of some of them along the way. At first it looks like a romance anime with the little twist of your lost childhood friend drama. However, then a genie appears and Arajin (becomes Deku combined with Saitama) deals one ending punch to his "enemies" and that is it. Remember how I mentioned loosing virginity? Yeah, well, I think that was there just so Arajin could scream "I want to loose my virginity!" before every merge as a joke.
His strength makes Matakara believe that Arajin really can become (or already is) a Honki person and that's why he won't stop pestering Arajin. And Marito sees this strength as a funny little game for his sick need of having fun fights - that is why he is always trying to fight Ken-chan, the head of the other squad.
Arajin tries to not get mixed up with either of them, but he does agree to go with Marito because of his sister. She turns out to have incestuous feelings for him.

Ok, stopping there and moving on. Matakara has a brother. He comes up suddenly. We find out he is in prison and that on the day he is supposed to be freed, he is killed/gravely injured. It felt like they only used him for Matakara's backstory purposes.

Then a new character appears. Akutarou, a pretty boy with blue hair that has few screws loose. He is such a weirdo and he only comes in to mix the cards and introduce a new special character, Ichiya. (Ichiya and Senya, I was thinking about those names for a while now. Aren't those numbers? Ichi & Sen, 1 and 1000... hmm.) Ichiya is another genie that has a beef with Senya. He posses Matakara rather than Akutarou, because Matakara is stronger. That results into Matakara changing completely and beating one ass after another. No one recognizes him, but thank god for petty Pretty boy, who is so mad, so he tells Arajin what happened. Suddenly, Senya disappears because he is haunted by his & Ichiya's past.
Arajin still makes Senya merge with him, insisting that he needs to bring his friend back. So they do merge, and we find out what this is all about. Ichiya and Senya knew each other from kids, and they were training together. Ichiya unfortunately has an illness that is killing him. But he doesn't want to die like that, he wants to be killed by Senya.

And remember Jasmin-chan? Well, this joke was in every episode. The man was visiting, always asking for her. Until one day they argued and he asked for another. But he came back and asked for forgiveness and then even went in all nice, as if he was going to propose. Next moment, he comes out with a literal CAT, running away with his beloved Jasmin-chan.

Those are the main plotlines. From my writing, you could say two things.
If you didn't watch it, you might think. Wow! What a good, interesting, relationship heavy story.
If you watched it, my interpretation might be confusing and I left out some things.
My problem is that if this was the main story, it was quite good just with the exception of a few plots that did not need to be in the story at all. I have three theories:

1. the authors thought it would be funny
2. they didn't know what to do with the empty space between the important episodes
3. they thought the story lacked

Things were dragging so so much. There was this one episode that had SO much happening, that nothing got resolved. We just watched three "prologues". There were episodes, that felt like fillers. Plot lines were jumping at us one after another, backstories seemed to be random, and even in the end some things just... still don't make sense. Questions are left unanswered.
Also, Arajin becomes a Honki person. But by that point, you even forget what a Honki person is.

The worst part about this is, that I would totally watch another 10 season of this. It's great, it's perfect... It's just... the authors need to realize what they want this anime to be. (Even though now is a little too late.)

Animation:
The animation was really really great. You have to have it in you, if you're doing an action anime, depending so much on fighting. In this aspect, BUCCHIGIRI?! really shines. The animation is very smooth, it looks good and special effects are made tastefully. And when Akutarou moves, it's soo smooth...!

Art:
Again, can't praise this enough. This anime has that 90ties feel I love in anime. It is great in quality, but it feels old-timey almost. The character design is very unique, the color combinations, the piercings, outfits... They are really thought through. There is nothing that doesn't look good.
Even though it's not visually-heavy when it comes to backgrounds, there are few shots and places that look just chef's kiss.

Characters:
This might be a bit too messy, but I said a lot in the "Story" section.
Our main character Arajin... well, I didn't notice any great character development, he just did a 180° turn during the last episode, but that was it. I don't know if that is genius or not.
Mahoro seemed like a very interesting character and I liked the double face she had. That girl would do everything for her brother... for better, for worse, for richer, for poorer, in sickness and in health.
Most of the background characters seemed like they would be fun to hang around, but they just didn't have enough focus on them. And that might not be such a bad thing, because this anime focused on silly stuff too much. (Man, see, why didn't this occur to me. If BUCCHIGIRI?! had 24 episode, or at least two cours, it would be 10/10. They just needed more screentime to be able to focus on ALL the stuff they want to show us. Man...)

Music:
I said it already, BUCCHIGIRI?!'s soundtrack had a strange mix of Arabic & Japanese and it worked SO WELL.
Opening - This might be the best opening I heard this season. It's so funny, it's catchy and the visuals are great too.
Ending - The same freaking story. So funny in how simple it is, and I wish I could learn all the words :D
Insert - there were a few insert songs, but none of them really stuck to me. Not because they were bad, they were fine. Just... if you're focused on trying to catch everything that is happening, you end up missing a thing or two...

Entertainment value:
BUCCHIGIRI?! is so close to perfection, it's not even funny anymore. Everything worked great, there was nothing bad about it. And that's what makes me mad the most. If they fucked up the animation, if it looked as bad as Cherry Magic!... I would shit on this show even more. But this isn't "hated hated HATED it" critique, this is more like a sad cry for help, because I just wish the story was more clean and clear.
Overall, I think everyone should give this show a change. Some might find it even more entertaining, some might disagree with my opinion and I doubt there will be anyone who will hate this show.
Maybe we get more content later and some things will get the ending they deserve. Just because Arajin became a Honki person, that doesn't mean the story is over right? There were too many plot lines for this to be a satisfying end...

Conclusion: recommended!!

but leaning towards "absolutely mixed feelings" ...