Instructions
Play through the game until you are between Hunter Rank 4 and 6. Once you reach this rank, speak with the elder at the guild hall in Pokke Village, to get HR4 and HR6 missions. These are high-ranking missions that have the best chance of rewarding you with a Giadrome Claw.
Complete the HR4 gathering mission in the Snowy Mountains and the HR4 hunting mission called, "A True Foe - The Giadrome!" While on these missions, you will encounter a Giadrome. Defeat the Giadrome and carve it, for a chance to get a claw.
Speak with the woman in green in the guild hall to get G-rank Giadrome missions. These quests specifically deal with high-level Giadromes, so you are almost guaranteed to get at least one Giadrome Claw by completing these missions.