For my play through I chose Helena's Defensive Type' Deck. You unlock her after playing through the game once.
On your very first battle. We're going to Summon the Griffin and playing only blue cards and ending your turn with
.
There is no tracker that I am aware. Count the cards ending your turn as necessary. MAKE SURE YOU DO AT LEAST 101 because as the achievement says 'OVER 100 cards in a single battle'.
Once you hit 101 cards played you can end the battle and it will pop afterward. As sorininf said:
"All the cards you can play, cost you each 1 mana. So you can finish after 20 turns."
Please comment or write me if I can be of more help!
credit to Jameswoo
just switch from defence to attack after turn 20, defeat the monster to end the battle and the achievement will pop after the battle