It's quite fun. I won't keep the episodes and it's not strong enough for an actual recommendation, but I had a laugh.
The show's only real disappointment, for me, is that it wimps out on its premise. I loved ep.1. Someone's assassinated a bunch of famous historical figures and so replacements have been found... from criminals who were going to be executed. This rabble are going to pretend to be stand-in leaders of the Shinsengumi (police cum death squads in 1860s Kyoto, a time of political instability). These criminals include a street punk who thinks samurai are evil and attacks them on sight (I love him already), an underworld hit man and a gangster whose first act on going out on street patrol is to start pickpocketing the passers-by.
On closer examination, though, it turns out that our anti-heroes are almost all nice underneath. (Although it takes a long time to start thawing out the underworld hit man, who's killed hundreds of people and is fond of torture.) It's hard to believe that they'd facing a death sentence. Ichibanboshi... okay, yes, he tries to kill samurai on sight. They're the ones who'd been going to behead him. Sakuya the hit man... yup, he deserves it. The others, though? Akira's a cross-dressing woman. Sougen is mildly sinister but a brilliant doctor who'd never actually do anything bad. Suzuran's a monk. Bou is big, fat and simple-minded. (Imagine a dozier version of Asterix's friend Obelix.) I suppose I could just about buy it with Gyatarou, who's clearly a lifelong criminal and scumbag... but even he's best friends with all the street children and helps distribute food and keep them alive.
An edgier version of this show could have embraced its Dirty Dozen premise and had subversive fun with the idea of replacing real historical figures with disturbing criminals who believe in murdering samurai on sight. That actual show isn't doing any of that. It's a laugh. It's hot-blooded shounen adventure, with an idiot protagonist who has Yu-Gi-Oh hair and whose idea of tactics is "CHARGE IN!!!!" (They make him their commander.)
That said, though, it's still fun. The characterisation is simplistic, but they're quite funny and the character designs are full of life. Akira's awkward relationship with her own femininity made me laugh. Sakuya's story arc is exactly what you think it's going to be, but it's still a meaningful journey for him. Ichibanboshi's stubbornness regarding his brother eventually pays off, albeit not with exactly the outcome he'd wanted. The baddies are cartoonish, but that's the kind of show this is and at least there's plenty of energy, death and killing.
I also like the show's politics. The idiot baddies are loyalists who claim they're the most loyal to the emperor and want to kill/expel all foreigners. It's pointed out to them that this is stupid and that the modern age will piss all over them. They're too macho to listen. Ultimately, the show draws a line from them to ultra-nationalists who want to start a war (which was a real thing and led to the Japanese aggression and atrocities of World War Two). Samurai dramas and this historical era in particular can easily become a vehicle for old-fashioned political sentiments, but this show has absolutely no time for all that and indeed is putting the boot into them.
The title's disastrous in both languages, though. I'd never have touched this show if I hadn't had a policy of watching all anime first episodes, because anything called "Bakumatsu Bad Boys" sounded like garbage. As for "bucchigire", that could be translated as "lose your shit" or "become uncontrollably angry". The last time I heard "bucchigire" in real life was when Tomoko was describing the behaviour of our five-year-old daughter who'd thrown a tantrum in the bath because she couldn't make a sculpture from soap bubbles. So that's roughly the level of maturity I'd been expecting.
I see no reason to rewatch this show... but it's fun and unashamed of its own silliness. Shinsengumi in a speedboat. That's the kind of show we're talking about here. Loud, colourful characters act like idiots and beat the baddies. I enjoyed it.