Here is the full list of all 21 Elemental Heroes achievements.
Collect 2500 crystals
Collect 2500 gems
Collect 4000 of ore
Collect 4000 of wood
Win 50 PVP battles
Loose 50 PVP battles
Surrender 20 PVP battles
Collect 100 card charges
Deal 1 000 000 of damage points
Receive 1 000 000 of damage points
Dodge 250 physical attacks
Reach 35th Level
Deal 10 000 000 of damage to Raid Boss
Kill 100 3rd Portal Bosses
Purchase 4 cards
Purchase 5 spells
Purchase 60 card charges
Collect 1000 diamonds
Collect 5 000 000 of gold
Send 100 gifts to friends
End 10 battles with both sides loosing all units