I started a TAS of this game a long time ago.
You can find it here:
http://dehacked.2y.net/microstorage.php/info/2403/Kuwaga_-_Mario_no_Super_Picross.smv
You can solve those puzzles really fast because there are two players and two buttons to hit a square with per player. So it's possible to hit up to 2 squares every frame. But you have to move in zig zag lines, as you can't go into the same direction for two consecutive frames because the game would obviously think you just didn't let go of the button.
Holding up to 6 buttons using frame advance can be quite annoying, so I wrote a major part of this WIP in hex. Finding the fastest solution can be quite troublesome too, but I'm quite confident that you can't improve any of the levels I did.
However, I'm not going to work on this anymore. The reason for this is something I noticed while doing stage 1-I. 54 frames is the amount of time you need hitting all squares of a 10x10 puzzle. It took me like a whole day, I think, to come up with a 53 frame solution for 1-I. Then, after I had rewritten the level in hex, I tried to start the next level one frame earlier, but guess what. Solving the puzzle one frame faster produces 2 frames of additional lag. So the 54 frame solution is actually faster.
I also tried to write a program which would find the solutions and write the hex code for me. But my algorithm sucks and it doesn't terminate on larger levels even after more than 24 hours. There has to be a better algorithm because I'm able to do better than my program, but I also suck at "reading my mind" to find the algorithm there. I guess a good algorithm would be to search the levels for basic overlapping patterns like two square thick lines, stairs or something like that, but I'm too lazy to do it. So I finally gave up. ^^
If anybody wants to continue this run, just do it.
