Can’t Get Gratitude Crystal from Peatrice

You get the feathers by catching the Chirri with the Bug Catching Net.

Now I know you said it, catching them is hard, but it's actually easy once you know the secret.

To be able to catch anything that could be caught, you need to sneak up on the target (i.e., walk up to it) and swing your net at it. It's easiest to swing sideways leading with the Wii Remote turned sideways. This applies to anything that is evasive or would otherwise run/fly away.

What I would do is sneak up to it with your net out and touching the target. Once you do that, swipe and it should be yours.

Here's a video demonstrating how you could do it:

There are 15.

From this guide:

Individual Gratitude Crystals (15 Gratitude Crystals)

NOTE: There are 15 individual gratitude crystals that can only be found at night time. Since you cannot fly around on your Loftwing during the nighttime, these gratitude crystals can only be collected at locations that have beds where you can go to sleep. Once you obtain the Master Sword, you can gain the ability to dowse for Gratitude Crystals. You can also grab these crystals using the beetle.

• Found within Link's Room on the desk.
• On the second floor of the Knight Academy, there is a Gratitude Crystal at the north part of the hallway.
• Inside of the Sparring Hall, there is a Gratitude Crystal up in the raftors. You will need to have the Beetle in order to get this crystal.
• Just south of the Knight Academy and down the steps, you'll find a windmill. There is small opening here and you can climb down the vines to get the Gratitude Crystal.
• Inside of Parrow and Orielle's house just south of the Bazaar. The crystal can be found at the corner of the room.
• Just north of the Bazaar at the lower lever where there are wooden planks. The Gratitude Crystal is nearby.
• A crystal can be found at the base of the Light Tower at the south end of Skyloft.
• Go through the Waterfall Cave and once you reach the exit, you'll find the Gratitude Crystal just to the left of the Bird Statue.
• Right next to the previous crystal, this one can be found in the small cavern where Link's Loftwing was being held at the beginning of the game.
• Near a bush and tree by the large pumpkin patch at the east end of Skyloft.
• The large waterfall at the northeast part of Skyloft has a Gratitude Crystal. You'll need either the Clawshots to climb up or you'll ned the Quick Beetle to reach this Gratitude Crystal.
• Grapple up to the chimney located above the Knight Academy. You can sneak into Zelda's room where you will find the Gratitude Crystal.
• A Gratitude Crystal can be found within the storage shed on the Pumpkin Landing.
• A crystal can be easily found on the second floor of the Lumpy Pumpkin at night time.
• Fall asleep using the bed that is on Beetle's Air Shop. You will awaken on Beetle Island. Go outside and there is gratitude crystal at the top of Beetle's ship. You can use the beetle to snag this Gratitude Crystal.