Here is the full list of all 21 Elemental Heroes achievements.
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 2500 crystals
Collect 2500 gems
Collect 4000 of ore
Collect 4000 of wood
Collect 5 000 000 of gold
Send 100 gifts to friends
End 10 battles with both sides loosing all units