I'm willing to believe that sub 1 is possible. Did a blind race of it the other day, and I made plenty of mistakes, but still netted around a 1:50.
As far as original boss order goes, fuse's ability is way too good to not get early. Crypt's is decent, and same with Virus's. I'll play it again when I get time.
EDIT (9/19): Played around with the game today. Found out you can softlock if you screen transition while in the middle of using Fuse Man's ability. Can't even pause or anything. I have difficulty wanting to run a game with programming errors that prevent progression. If they get fixed, great. If not...
I got 1:05:00 the other day. I had plenty of deaths. I still think sub 1 is possible. I might even try to get a video of it at some point. >_> In all my practice runs (including the above), I was able to get Beat before I finished 8 robos. Beat is extremely helpful against each of the 5 bosses after the 8. I wish he was more useful in Justice 2's boss though....
Text progression is slower. However, it's less likely to softlock, plus there aren't as many invincibility frames in between hits on normal enemies, so you can kill them faster.
The 1:05:00 was done on the older version. I have yet to try a serious run on newest version, although the practice run I did last night was about 1:07ish.
What is a better stragagy for the first part of justice man 2 boss? Getting on the ice cubes and firing charge shots or using rush coil to spam reguler shots?
You can either use Rush Coil or Pulse's ability. I prefer the latter, but that boss is terrible no matter what. There's too much RNG on that fight to rely on jumping on the ice cube, but if the cube shots were constant, charged buster shots would be faster.
I don't really speedrun this game much anymore, but there was a recent update on the game within the last week. The main reason I stopped running this was because there was (and still is) no definable difficulty to go with. You can change parts of difficulty, such as # of checkpoints, spike damage, and spike effects (mm1 spikes, mm2 spikes, etc.). There's no real way to define a category for the game, so you can pretty much pick whatever you want and go with it for running.
The changes are numerous, but the ones that stuck out to me most were about sliding off ledges and boss weaknesses. You no longer float enough to slide from one even platform to the next (over a pit); you have to jump now. Every boss now has a weakness, and some bosses have periods where they are more vulnerable now (taking out some of the rng factor in the game).
I might play this new update again soon, but thought I'd clear up my reason for not speedrunning this game.