Hmm the 3mins last season was pretty easy to do solo. It was harder the season before though(but still doable), powercreep and all that, but outgearing T10 that you one shot even elites didn't take nearly as much effort, and then it was a matter of finding a decent enough rift for it(high density, high elite numbers, relatively open maps). Can take a while, but not bad.
2mins on the other hand is annoying as shit, and I'd call that one borderline impossible without a group. There's obviously a very large difference between 2 and 3mins. Might be doable on some builds and a lot of good RNG(I'm thinking like that explosion wizard build that kills everything without having to stop, possibly WD chicken+autocast locust arachyr with the buff, this kind of stuff, but I think like UE6 multi DH for example would be too slow due to the constant stuttering to kill stuff, even if the clearspeed is insane in general).
That said just like every season, you don't need to do all the conquests, thank god, so you can skip that shit one. You still need a 3mins clear for the last step of the season journey for the stash tab, but I've done it the past 2 seasons and it's doable with any class nowadays, even Crusader which I think had trouble before they made all the S5 changes.
List of conquests:
1. Complete a T10 rift within 2 minutes
2. Level 3 legendary gems to 65
3. Reach Greater Rift 75 solo
4. Kill 350+ monsters in T10 Cursed Chest event
5. Kill all bosses on T10 in under 20 minutes
And the same in HC obviously. Out of these, reaching GR solo and leveling gems are the easiest and most natural to complete, which leaves one to pick out of the other 3 to get the 3 conquests season journey objective.
The kill 350+ monsters in a cursed chest sounds kinda hard to do solo, although it'd depend on your build maybe? That sounds like a lot of mobs though, you'd need very high damage and very high aoe at the same time. Something like UE or Marauder DH(with multishot) for example would clear the entire screen over and over easily, while some other builds would have more trouble due to not having as much reach(thinking most WD builds for example don't have nearly as large constant aoes).
The kill all bosses was used during S4 and was fairly easy, however it was under 30mins back then, I think I took about 24mins on my WD on my first try. It seems like it'd be doable solo, but only with very high movement, and also a very high damage build to kill the bosses instantly. It is however extremely easy to do in a group, even of 2 people, since a large part of the time spent on this conquest is finding shit like the act5 bosses location. Still I think classes with very high movement speed like DH/WD/Wiz and potentially Crusader are at a major advantage, while monk/barb would have a lot more trouble even though they have decent movespeed, since the key is finding stuff.
And finally the 2mins one which I think you'd need at least 3 or 4people to do AND fish for rifts. Definitely the useless one unless you're just rifting in groups to begin with, then you can just kinda get it while farming for keys.