Here is the full list of all 10 AXYOS: Battlecards achievements.
Win for each of the factions
Win 10 times in a row
Win 5 times in a row
Winning without using the crafting cards
Make a move in less than 3 seconds 5 times in a row
Victory without damage to your Axyos
Win in less than 15 moves
Win without using of ultimative skill
Sell 5 cards during the fight and win
During the battle use kraft cards 20 times