Beedle's Horned Colossus Beetle
Beedle's Horned Colossus Beetle is a side-quest in Skyward Sword.
Speak With Strich On Bug Rock
After defeating Bilocyte, the Thunderhead will clear up and look much less menacing. Strich flew in to investigate and found an island which he swears is a truly awesome place to hunt for bugs. He has a game available for you which you may want to at least practice with.
Link talking to Strich about his bugs
Something's Bugging Him... (Optional)
Only after you've spoken with Strich on Bug Rock, you can return to Skyloft and enter Beedle's Air Shop. Speak with Beedle if you wish; he merely says that he wants to talk with you later that night.
Beedle telling Link to visit him at night
Sleep on the bed in Beedle's Air Shop to go to his island. Go outside and speak with him next to the fire to hear of his dire situation. His prized Beetle is missing! Where could it possibly be? Hmm... Sleep on the bed in the Air Shop to return to Skyloft.
Bug Hunting Challenge
Head back to Bug Rock and confront Strich about it. He'll rant for a bit about how happy he is that he's found such a rare bug, but once you break the news to him, he's reluctant to give it up so easily. He suggests that you take the expert course for his bug hunting challenge, and he'll even reduce the price for this event. Complete his game within the time limit and he'll fork over the Horned Colossus Beetle.
Return to Skyloft, sleep on the bed in the Air Shop, then chat with Beedle by the fire. With his prized pet back, Beedle is so overjoyed that he will give you five Gratitude Crystals! Additionally, he'll reduce the price of the next thing you buy in his shop to half off.
Link giving Beedle his prized Horned Colossus Beetle