Here is the full list of all 20 Duel of Summoners: The Mabinogi Trading Card Game achievements.
Challenge the Cat Merchant in a duel and win
Join 1 Internet Normal Battle
Register a deck at the Draft Arena
Sell 1 card to the Card Appraiser
Create a deck from 'My Card' and save
Make the first trade with the Cat Merchant.
Started the game.
First time registering after starting the game
Claimed 'Starter Deck' from the Shop
Start the Tutorial.
Purchase booster for the first time at the Shop
Obtain 5 cards from a booster and obtain Sarah
Player reached level 2
Clear Tutorial 1 and unlock Sarah
Cleared up to Story Mode Episode 3: But Elf
Cleared up to Story Mode Episode 4: The Meeting
Cleared up to Story Mode Episode 6: Doctor Blin Blin
Visit the Cat Shop and purchase 1 card
Clear all of Chapter 1 (10 Episodes) in Story Mode.