Here is the full list of all 27 The Gem Collector trophies - there are 10 bronze, 9 silver, 7 gold and 1 platinum.
Collect all trophies in The Gem Collector.
Collect all Money and Defeat all enemies in Sower's Seams. (World 5)
Collect all Gems in Sower's Seams. (World 5)
Collect all Keys in Sower's Seams. (World 5)
Raid Dinglah's Treasure Hoard. Collect the key, all money, and all gems.
Collect the Key on the secret thank you level after the credits.
Defeat Dinglah.
Collect all Keys in Silhouette Sky. (World 4)
Collect all Money and Defeat all enemies in Silhouette Sky. (World 4)
Collect all Gems in Silhouette Sky. (World 4)
Use Sun Beams to light both torches and open the door. (4-1)
Collect all Money and Defeat all enemies in Deep Cavern. (World 3)
Collect all Gems in Deep Cavern. (World 3)
Collect all Keys in Deep Cavern. (World 3)
Use Jasper to knock down a normal sized gem from a rope onto Nomi's head before it hits the ground.
Collect all Money and Defeat all enemies in Gear Fields. (World 2)
Collect all Keys in Gear Fields. (World 2)
Collect all Gems in Gear Fields. (World 2)
Use electric beams to connect the current and open the door. (2-1)
Collect all Keys in Wistful Sands. (World 1)
Collect all Money and Defeat all enemies in Wistful Sands. (World 1)
Collect all Gems in Wistful Sands. (World 1)
Stand by a pile of snowballs in the first bonus level and throw out snowballs instead of magic beams.
Use Jasper to trigger a lever. (1-2)
Collect the Key on 1-1 with 5 hearts.
Hit a Checkpoint.
Collect the Key on the Tutorial Level.