Looks like this game has been abandoned twice already... It's time for a third time :D
I just started trying to TAS it and played first two levels skipping training.
I was aiming for minimum time between the moment I gain controls over stick and the moment it reached destination without taking damage, BUT I hit the walls while inside safe (starting) area to adjust my position, and that really helps.
Grassland-1 time: 0'05"78 on timer (record time: 0'05"76, one frame faster, but I believe that was gained by waiting in the start area, and that adds unneceseary play time). I hit the wall twice while in start area to aviod waiting at the end of the level. I could not get 0'05'76 or less no matter how hard I tried(~10 different attempts), my path seems to be optimal.
Grassland-2 time: 0'10"78 on timer (record time: 0'10'83). Once again no waiting at the start, but position is adjusted by hitting wall in the safe area. I've got this result on second attempt and I find it pretty good. Maybe few frames can be cut off.
EDIT: Yay, microstorage works again, and here is movie file:
http://dehacked.2y.net/microstorage.php/info/3332/kuru1-2.vbm