Here is the full list of all 18 Memory Battle achievements.
Win your first match.
Win largest and hardest battle with 3 fighters.
Win largest and hardest battle with only 1 fighter remaining.
Win largest battle under 5 minutes.
Be defeated in smallest and easiest battle with 30 fighters.
Be defeated 100 times.
Conquer winterland.
Win 10 smallest matches. (4x4)
Win 10 small matches. (5x5)
Win 10 large matches. (7x7)
Win 10 largest matches. (8x8)
Win at all battlefields.
Win 10 smallest battles. (4x4)
Win 10 small battles. (5x5)
Win 10 large battles. (7x7)
Win 10 largest battles. (8x8)
Win 100 battles.
Complete all quests.