Not entirely sure if you can split kill it, the achievement has a checklist that ticks off each boss kill individually. Assume if you aren't in for the kill it doesn't count for you. Didn't bother testing though.
Either way doesn't matter, it's not that hard if you setup correctly. Like I mentioned before we just used a wizard with the teleport wand and we completed it in 20 minutes. Minus Act 5 he made it to each boss in less than a minute. Some of the bosses he reached in less than 10 seconds.
Actually on that topic, Act 5 alone took over half our time. Something like 13 minutes, the maps are just massive and all the fights are longer because immunity phases with monologues and shit (or in the case of Adria constantly teleporting). After that it was smooth sailing.
You can split to find the bosses. A large part of the conquest is the time you spend running around finding the bosses that aren't obvious(arachnae and the act5 stuff mostly). You split, each find a boss, TP out, then TP to whoever else without using up your TP. This way once you kill a boss, you TP to someone who's in town, go into your portal back to another boss, and everyone TPs on you. Massively reduces the time spent.
That said if you have very good movement speed abilities and good killing speed, it's entirely doable solo, especially since you can switch gear around. Getting gloves of worship(either cubed or equipped if you can afford it without breaking your set) and starting in act4 to check for shrines and hope you get fleeting or empowered is a good way to start, then you can use the bracers that speed you up when you break stuff and krelm belt and so on.
As a WD I had no trouble doing it solo even before I was at my GR60 gear level. The only thing I needed for it was majuma set and replaced piranhado with angry chicken(piranhado doesn't do a whole lot against bosses anyway) and then I just switched weapons everytime I got to the boss, had like 7 or 8mins to spare at the end, and didn't even get particularily good RNG on the act5 bosses position(also on ghom I ran the wrong way for a while). You still need good enough gear you can kill the bosses quick though, I wasn't like crappy geared, typical helltooth gear with a non ancient suwong and legendary gems were around 40 already and I speced both piercing veil and confidence ritual for more damage.
I'm sure barbs, DH and Wizards would have no issues, monk I don't really know if they can sustain speed over long periods of time, I think there's a set for dashing around without the charges though so assuming that's viable for killing stuff, it'd work, and crusader would as usual need a stupid amount of cdr+steed weapon to even have a chance, but in general the class is slow as shit so I don't know. A shield bash roland spec would melt the bosses I would think however, possibly faster than every other classes, so you might make up time like this.
