This is the part where most people start getting stuck on. And give up on. It's moments like these where you wonder why you wasted your time buying this game. But we're here, so whatever. Let's continue.
Just so you know I'm redoing the whole game just to write this blasted thing. And I have no idea how to use this website so please excuse me.
After another long winded cut scene you arrive to the next map, Muse River. Here you'll see 5 flowers and a red haired girl in the river. The girl has you dragonfly, and she doesn't want to give it back till you help her fix the bridge. What an irritating girl.
If you tapped on the flowers, you'll notice they produce a music note and a part of a white bridge appears on the left. If you talk to her, she'll tell you that you need to use the flowers and copy her music piece to make the bridge appear entirely to cross. Unfortunately, because the girl didn't bother to take care of them, one of the important flowers has died. Without it you cannot complete the puzzle and head north across the bridge. But let's ignore the flower for the time being and head over to the next map.
When you reach the next map, a cut scene later and you'll be in the Cave of Anthea and Arachne. Another dragonfly is here, stuck on Arachne's web. But the blasted old lady won't let you disturb her precious boy. To get the dragonfly, you need to fix the web that got broken somehow in the time limit. But Anthea's a cheating bstrd and added hardly any sand to the hourglass, making it almost impossible to complete. This will be solved later though let's focus on the flowers first.
Now at the next map, you'll be in the beginnings of the cave. This is where the important things begin.
1) Walk over to the dripping water. Upon looking at it, the dying flower next to it will bloom. Use the cup to collect the water for our dying flower.
2) Pick up the small rock on the ground too. That'll be important for later.
If you try to go further, Alice will deny you of entry. That's because to go further you'll need a lit candle to light up the cave, which are currently all unlit at the corner of the map. They'll only light up when you finish the first puzzle.
Now back to the river!
3) Use the water on the flower. It'll bloom and now you can start on your tunes. You'll need to follow the song the girl plays to create the bridge. To make your life easier, I went to ask Sloth for the answer and because his drawings sucks crap I replaced the drawings with the actual flowers
Here's the drawing!
I know the picture looks weird but that's because they drew it like a music piece, so for those who don't understand it just follow the blue arrow. Surely that's more understandable.
Now that the bridge is up, a blue dragonfly will appear from it. Follow the instructions and use the necklace on the dragonfly.
You now have your first dragonfly.
Onwards to the next puzzle!