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