I watched your run, then Genisto's 1 player run, and half of your run again to make sure I was seeing things correctly.
Your run overall is pretty good, but when there's Genisto's run out there, it's really hard to accept this one. I really liked the first stage and thought that there wasn't really anything that could be improved, other than possibly the boss fight, but I'm not sure about that one.
But here's a list of possible improvements:
Somehow Genisto was able to shoot out more or less constant streams with his spread shot. It seems to help out a whole lot, especially on the base levels.
With the 2 player run, it's vital to be in control of lag. It slows down your run a lot, and it's the main reason why it's probably not possible to surpass the 1 player run in speed, though if it was minimized by shooting the correct things and not shooting when unneccesary, it should be possible to bring the times closer together. So it would probably be wise to, say, shoot the crowds of guys in the base with one character when there's a lot of lag caused by them.
There's a lot of unneccesary shooting in many levels. It really adds to the lag. It's a whole lot harder to only take neccesary shots in a two player run, especially with the confusion on whether or not it's better to kill an enemy or not based on whether it causes more lag to kill it from the bullet lag or just leave it alone to clutter the screen. Though I think that a simple case may be the waterfall boss. If it's a set amount of time for it to open its mouth, regardless of when its arms are killed, both players shouldn't shoot at once, since it causes a lot of lag. Otherwise, I'm not totally sure what's best. It's a really difficult thing to do, but I think it's needed in this case, because comparisons to Genisto's 1 player run are inevitable. The only exception seems to be in base levels, where I think it's a factor in making a more singular stream, though I'm not certain.
In levels such as the energy zone and warehouse, it may or may not be faster to have the one in front wait for a moment so that they coincide, so that the timing with the lasers are handled better (I'm not sure about that one) and so that the boost of speed from the cart can be used (not sure whether this would save time either)
Genisto is able to jump over the spike things that come down on that long stretch near the end of the warehouse, and it would save time, as you said. Sorry, though, I don't know how to do it. But it must be possible somehow.
On the waterfall level, it saves time to not have both characters jump at the same time. For example, on the first cliff, you run until both characters are able to make it onto the first cliff. If you have the one in front jump first and barely make it onto the cliff then have the second character jump when he can barely make it onto the platform, it would save time. There are a few places like that, mostly the beginning cliff and the area around the last moving platform, that can save time. And I'd say that if you save so much time with the first player that the second one ends up dying as the screen scrolls up quickly to the boss, that's fine. I think that death would be appreciated if it happened, since it would really show that you're doing it as fast as possible, but I don't think that death would happen if both players move as quickly as possible. But in all levels, don't worry if the second player falls behind. Just forcus on the first player moving as quickly as possible. Have the second player worry about lag and such. Just have the first player move as ideally as possible without adding too much lag.
In other words, it'll be a whole huge headache to try to optimize the run. I think you did a pretty good job, and if this was made about two years ago, it probably would be accepted. It's just that there have been so many runs and so many optimizations in that amount of time that it's really hard for most people to get a run that'll be accepted when compared to runs of experts like Genisto. =( But if those changes are made (obviously not an easy task by any stretch of the imagination, and would probably increase the rerecord count about tenfold), I would joyfully choose Yes, and I think most other people would as well. Because it would be great to see. As it is now, though, I don't think it's optimized enough to be accepted. It was a good attempt, though. And it's something that someone really should be working on, so I'm glad you chose it. =)