Yay! I finally did it! Now for the inside scoop on how to do this:
Part 1: It's pretty straight foward. Start running immediately and keep to the left to nab the first blue butterfly and swerve between the two red butterflies. Before you nab the second blue butterfly the timer will finally start. just nab it and keep going. There's an easy to nab blue butterfly near the chest where the path takes a left and one more before the really hard part begins. To get by the swarm here, you need to move upward while avoiding the red butterfly there, and by the time you accomplish this that buttefly in the middle which I'm sure gave you much trouble will have moved far enough to the right for you to sqeeze through and grab the blue butterfly afterward. Dodge the remaining red butterfly (not hard) and run until the path turns a little toward you. You will now see the final blue butterfly and you can nab it easily. Part one completed! Don't forget the treasure chest you won (I got a Teleport sphere, you might get something different) and backtrack to the second part of the game.
Part 2: I suggest you save before you attempt this because you never know if there is going to be a power outage and you don't want all that hard work to go to waste. You don't have to, though.
This one can be tricky, but with my tips it should be easier than the first one. First move behind you and nab that easy to miss blue butterfly. Keep toward the right coming back to avoid the hidden red butterfly. Dodge the butterfly on the right side of the path and nab the blue one in the center. After dodging the butterflies you start to head upward. Keep toward the right to nab the blue butterfly and keep to that side of the branch to avoid the next two. Then cross sides to avoid the next one, cross sides after that, and cross sides yet again to avoid that last butterfly. Go under the overlying branch and dodge the red butterfly that greets you. Keep going and keep to the right to get another butterfly. I think the butterfly coming up can be avoided by crossing sides, but I forgot. Dodge the hard to see moving butterfly in the shaded part of the branch and keep toward the right to avoid the next one. After that simply nab the two remaining ones and avoid that last butterfly which is pretty hard to hit.
I hope I helped!