Here is the full list of all 12 Gem Legends (EU) trophies - there are 7 bronze, 4 silver and 1 gold.
Lower 20 diamonds on levels with mechanics "Lower diamond"
Activate 3 super bombs at any level
Simultaneously detonate 5 bombs at any level
Destroy 4 stones with explosion
Remove 500 stones
Remove 500 tiles
Match 10 chips of the same color
Collect 20,000 points on any level
Complete main goal in 5 turns
Use 5 purchased for gold bonuses on a single level
Lower 3 diamons simultaneously on levels with mechanics "Lower diamond"
Complete all levels with the best result