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"
Use 5 purchased for gold bonuses on a single level
Activate 3 super bombs at any level
Remove 500 stones
Simultaneously detonate 5 bombs at any level
Lower 3 diamons simultaneously on levels with mechanics "Lower diamond"
Remove 500 tiles
Destroy 4 stones with explosion
Match 10 chips of the same color
Collect 20,000 points on any level
Complete main goal in 5 turns
Complete all levels with the best result