Here is the full list of all 30 Gems Kingdom achievements.
Play the first map
Play the second map
Play the third map
Play the fourth map
Play the 5th map
Play the 6th map
Play the 7th map
Play the 8th map
Play the 9th map
Play the 10th map
Play the 11th map
Play the 12th map
Play the 13th map
Play the 14th map
Play the 15th map
Play the 16th map
Play the 17th map
Play the 18th map
Play the 19th map
Play the 20th map
Play blitz mode
Play Gauntlet mode
Play Warfare mode
Play Endless mode
Finish the game as a warrior
Finish the game as an alchemist
Finish the game as a pirate
Finish the game as a summoner
Finish the game as a rogue
Finish the game as a priestess