1. Near the Seven-Heaven Statue on the right side of Mondstadt Dawn Winery: After teleporting to the Seven-Heaven Statue, look to the right. There are three crystal butterflies around that can be captured. Continuing forward, you can also find two crystal butterflies, and you can catch five in total.
2. Near the secret realm of Guyun Pavilion in Liyue: Looking back from the secret realm, three crystal butterflies will appear. Go to the cave entrance path on the right to find two more crystal butterflies.
3. The teleportation anchor point in the Serpent Cave in the underground mining area: Jump down from the teleportation anchor point in the Serpent Cave and use the Wings of Wind to glide. You can catch three crystal butterflies along the way.
4. Near the Qiji Cave in Liyue: Around the Qiji Cave in Liyue, some crystal butterflies often appear, which can be caught and obtained crystal cores.
5. Near the headquarters of the Knights of Mondstadt: Some crystal butterflies often appear on the trees near the headquarters of the Knights of Mondstadt. Players can use the character's climbing ability to catch them.
6. Near the Wind Dragon Observatory: In the territory surrounding the Wind Dragon Observatory, some crystal butterflies can often be found, and players can track them and capture them.
The above is the relevant content about how to quickly obtain the Genshin Impact Core. I hope it will be helpful to you!