Here is the full list of all 10 Duelyst achievements.
Complete your first 5 Quests.
Play your first game with a Friend.
Play your first 20 Ranked Ladder games.
Complete your first 10 games.
Complete your first Quest.
Complete your first 13 Quests.
Complete your first 100 Quests.
Collect one of every Common rarity card.
Complete your first 50 games.
Play 1 game with each of the six Factions.